Illustrations: Beehive (Nadene Naude, Andrew Pagram)
Photos: Shutterstock
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Maths and Me – Innovative Digital Resources
Maths and Me provides access to an extensive range of over 2,500 fun, innovative, easy-to-use and engaging FREE Interactive Digital Resources including editable planning documents and a full range of printables. All resources are central to the programme and integrated into lessons, providing rich learning opportunities for children, by encouraging active participation and positive engagement. Designed specifically for Maths and Me, with the key pedagogical practices in mind, the resources promote maths talk, allow for formative assessment, include cognitively challenging tasks, mathematical modeling and lots more.
The extensive range of digital resources include:
n Rich multimedia resources –engaging videos and animations
n Interactive classroom activities
n Virtual manipulatives
n Editable planning documents
n Printables
Explainer videos help pupils to understand key maths concepts and strategies
Classroom activities such as Concept Cartoons, Quick Images and Three-Act Tasks engage learners, support key pedagogies such as maths talk and playful learning, help pupils develop skills such as reasoning and allow for formative assessment.
access to a dedicated app with digital sources for pupils to use at home or in school on devices.
Engaging animations feature the Maths and Me characters in relatable maths-based real-life scenarios.
An extensive range of colourful printable resources can also be accessed via the platform, including Maths Language Cards and Manipulative Printables
Digital resources are accessed through an easy-to-use web platform.
Digital Resources for 6th Class, Unit 1: Place Value
1-2
1Place Value
3-4
2Decimal Numbers
53 Millions
64 Estimating and Rounding Numbers
7-8
5Positive and Negative Numbers
96 Positive and Negative Numbers on the Number Line
Do We Have a Base Ten System?
The Place Value System
What Value Does this Represent? (A)
What Value Does this Represent? (B)
Decimals
Same But Different –Numbers to Millions
How Big is a Million?
Which One Doesn’t Belong? – Estimating and Rounding Numbers
Rounding Numbers
Concept Cartoon, with Think-PairShare Concept Cartoon
Reason & Respond, with WriteHide-Show Video
Quick Images, with Write-HideShow Quick Images
Quick Images, with Write-HideShow Quick Images
Reason & Respond, with WriteHide-Show
Video
Reason & Respond, with ThinkPair-Share Slideshow
Reason & Respond, with WriteHide-Show
Video
Reason & Respond, with ThinkPair-Share Slideshow
Reason & Respond, with WriteHide-Show
Video
Which is the Greatest Value? Concept Cartoon, with Think-PairShare Concept Cartoon
The Elevator Three-Act Task Three-Act Task
Same But Different –Positive and Negative Numbers
Reason & Respond, with ThinkPair-Share Slideshow
Scan the QR code below to access a selection of our new digital resources for Maths and Me 5th and 6th Class:
FOR A DEMO OF THE NEW DIGITAL RESOURCES
Pupil’s Book Contents
Note: The contents shown indicate what is included in the full Pupil’s Book.
Unit 1: Place Value
Unit 2: Operations 1
Unit 3: Operations 2
Unit 4: Time
Review 1
Unit 5: Shapes and Angles
Unit 6: Fractions
Unit 7: Operations 3
Review 2
Unit 8: Fractions, Decimals and Percentages
Unit 9: Measuring 1
Unit 10: Data
Review 3
Unit 11: Money
Unit 12: Location and Transformation
Unit 13: Patterns, Rules and Relationships
Review 4
Unit 14: Expressions and Equations
Unit 15: Measuring 2
Unit 16: Ratio
Unit 17: Chance
Review 5 Let’s Try More Glossary
The Maths and Me Pupil’s Pack includes a Progress Assessment Booklet and the following inserts to support learning: mini-whiteboard with open-number line on reverse, spinners (for playing games) and a cut-out Fraction Wall.
Let’s talk!
Look at Jay. Do you agree? Why or why not?
With a partner, take turns to read these numbers aloud: 45,681 432·52 307,570
What is the value of the digit 5 in each of the numbers? In which number above does the digit 4 have (a) the greatest value, and (b) the least value?
Write each number using digits (standard form).
Remember! There must be 3 digits between each comma.
1. Two million, fifty-six thousand, five hundred and two
2. Three hundred and fifty-six and seven thousandths
3. Seven million, eighty-four thousand, seven hundred and eight
4. Nine hundred and ninety-two thousand, six hundred and nine
5. Eight million, five hundred and seventy thousand and nineteen
Our place value system extends infinitely in two directions towards very large numbers and very small numbers.
If you can read a 3-digit number, you can read any large number
Don’t forget to use zero as a placeholder where necessary.
6. Fifteen thousand, four hundred and eleven and twenty-five hundredths
7. Eighty-seven thousand, one hundred and fifty-six
8. One million, two hundred and ninety-nine, and four thousandths
2,056,502
C Let’s play! Wipeout!
Number of players: 2–6
You will need: calculator, mini-whiteboard, and marker per player
● To start, each player inputs a 7-digit number (any digits except 0) on their calculator and writes the number on their mini-whiteboard.
● A caller (perhaps the teacher) calls out a digit, for example, 6.
● Any player with a digit 6 on their calculator display wipes out only this digit, so that there is a 0 in its place. They record how they did it on their mini-whiteboard.
● Only one digit can be wiped out each time.
● The player who wipes out all their digits first wins the game.
Variation
● Play as above, but each player inputs a number with 3 decimal places (to thousandths) and 3 whole number places (to hundreds).
What is the greatest number of digits your calculator screen can display?
D Are these always (A), sometimes (S) or never (N) true?
1. Our place value system extends infinitely in two directions.
2. The digits in numbers are organised in groups of three.
3. The value of a digit depends on its position in the number
4. Numbers with a decimal point are smaller than whole numbers.
Is there any difference between the way large numbers are written in this book and the way they appear on your calculator display? Can you give examples to prove it?
5. As you move away from the decimal point, the value of each place is 10 times greater
6. If a digit is moved to the column to the right, the value of the digit is now 10 times greater
7. A number with more digits is always greater than a number with fewer digits.
8. Zeros do not affect the value of a number
Try this! Mystery numbers! What 7-digit numbers did they make?
Unit 1: Place Value. Days 1 and 2, Lesson 1
1. In Lexi's number, the nearest thousand is 6,476,000. The tens digit is half the millions digit. It is a multiple of 10. The hundreds digit is the same as the ones digit in the rounded number above.
2. In Dara's number, the tens digit is one third of the thousands digit. The hundred-thousands digit is double the tens digit. The digits from millions to thousands are all consecutive numbers. The thousands digit is even. All the remaining digits are multiplies of eight.
The number is The number is
Unit 1: Place Value. Days 1 and 2, Lesson 1
Decimal Numbers
What (a) decimal fraction, and (b) fraction (thousandths) is coloured? Where possible, express the answer in its simplest form.
In what (a) decimal fraction, and (b) fraction of each grid is uncoloured?
1. (a) (b)
3. (a) (b)
5. (a) (b)
In above, what…
2. (a) (b)
4. (a) (b)
6. (a) (b)
1. is the largest decimal fraction that is (a) coloured? (b) uncoloured?
2. is the smallest decimal fraction that is (a) coloured? (b) uncoloured?
3. decimal fraction is (a) greater than a half? (b) equal to 1 40 ?
Let’s talk!
If you add the number of coloured parts to the number of uncoloured parts in each grid in , what do you notice? Can you explain why this is so?
The children each coloured in part of a grid. Write as a decimal fraction the amount (a) coloured, and (b) uncoloured for each.
1. Mia coloured in 6 tenths, 4 hundredths and 2 thousandths. (a) (b)
2. Dara coloured in 28 hundredths. (a) (b)
3. Jay coloured in 37 thousandths. (a) (b)
4. Lexi coloured in 648 thousandths, and then rubbed out 6 hundredths. (a) (b)
Write the answers to these as decimals.
For 80 + 1 + 3 1,000, Lexi wrote 81·003
1. 3 + 5 10 + 7
+ 2 1,000 =
=
=
Write these as expanded fractions. For 0·935, Dara wrote 9 10 + 3
Write the number that each arrow is pointing to in (a) standard decimal form, and (b) fraction form.
=
Write the correct symbol (<, > or =) to make these true.
1,000 people attended a local food festival. Express each amount as a decimal fraction of the total attendees.
1. 235 of them wore hats.
2. 197 children attended.
3. 460 women attended.
4. Half of the women wore sunglasses.
Try this! Write these as decimal numbers. Explain your reasoning to another.
1: Place Value. Days 3 and 4, Lesson 2
1. A (a) (b)
B (a) (b)
C (a) (b)
Millions
Let’s talk!
Look at the numbers in these headlines. What do you notice? What do you wonder?
Why are the numbers written this way? What does ‘m’ stand for after the numbers? What else can ‘m’ stand for in maths?
€5.4m invested in local sports clubs
€4.4m raised for children’s charity Beach house sells for €3.25m
4 4m in full standard form is 4,400,000. What would the other numbers be in full standard form?
Look at the table and answer the questions.
1. In your copy, write out the population of each city in its full standard form.
2. Which of the cities has the…
(a) largest population?
(b) smallest population?
3. The population of which city is…
(a) just under five and a half million?
(b) almost eight and a half million?
(c) just less than ten million?
4. Approximately how many times greater is the population of Berlin than that of Dublin (city)?
Look at the table and answer the questions.
1. In your copy, write the area in sq km of each desert in millions.
2. Which of the deserts has the… (a) largest area?
(b) smallest area?
3. Complete this: The area of the Desert is just under twice the area of the Desert.
Try this! Lexi saw a maths fact that said 1 tonne = 1,000kg She then told Mia that there are a million grams in a tonne. With evidence, prove that Lexi is correct or incorrect.
Estimating and Rounding Numbers
Answer these.
1. Complete the table below by rounding each diameter to the nearest thousand km.
2. In the table, the diameter of which planet is…
(a) nearly fifty thousand km?
(b) just over fifty thousand km?
(c) approximately twelve thousand km?
(d) less than five thousand km?
(e) slightly less than one hundred and forty-three thousand km?
Planet Diameter (km) Rounded to the nearest thousand km
Mercury 4,879 (a)
Venus 12,104 (b)
Earth 12,756 (c)
Mars6,792 (d)
Jupiter 142,984 (e)
Saturn 120,536 (f)
Uranus 51,118 (g)
Neptune 49,528 (h)
Express each of these concert ticket sales rounded to the nearest tenth of a million. 1. €6,270,000
€9,719,500
Round each number to…
One of the planets is sometimes called ‘Earth’s twin’. Which one do you think it is? Why? 1. 81 295 2. 49.613
3. 67 055
4. 52.039
€5,684,500
5. 33 064 (a) one decimal place (b) two decimal places
Try this! Ring the number below that is closest to the number 1. What model could you use to prove your answer?
Positive and Negative Numbers
Let’s talk!
Which of the statements below describe positive numbers? Which describe negative numbers?
The temperature is 12°C above zero.
The temperature is 8°C below zero.
Mathsville United have scored 16 goals.
Aria’s bank account is overdrawn by €50.
Eva’s golf score was 1 over par.
Maggie lives 15 floors above the ground floor in an apartment block.
The Dead Sea is 423m below sea level.
Tanush has €30 in his bank account.
Sumtown United have not scored any goals, but have let in 15 goals.
Aaron’s golf score was 3 under par
Ben Nevis is 1,344m above sea level.
Shane parks his car 3 floors below the ground floor in his large office building
Use a positive or negative number to represent each of the statements in above.
Answer these.
1. Write the temperature of each thermometer
2. What is the highest temperature? °C
3. What is the lowest temperature? °C
4. Which temperature is the furthest from zero? °C
5. What would each of the temperatures be if they rose by 5 degrees Celsius?
6. What would each of the temperatures be if they fell by 5 degrees Celsius?
Try this! Research the average monthly temperature in January for some capital cities around the world. Identify two that have negative temperatures, and two that have positive temperatures. Answer these questions:
1. Which is the (a) hottest city? (b) coldest city?
2. What is the difference in temperature between them? °C
D Let’s play!
Number of players: 2
Number Paths Race
You will need: paperclip per player, deck of playing cards with picture cards and 6–10 cards removed
● To start, each player places their paperclip at zero on the number path below.
● Each player, in turn, turns over the top card.
● If the card is black, the player moves forwards that amount. If the card is red, the player moves back that amount.
● A player wins the game by being first to reach +15, or loses the game by being first to reach –15!
Positive and Negative on the Number Line
Identify the missing value indicated by each box.
Write the correct symbol (<, > or =) to make these true.
C Maths eyes
I’ll use a number line to help me.
1. What is the difference in degrees between the temperatures in…
(a) Dublin and Reykjavik? °C
(b) New York and Moscow? °C
(c) Ottawa and Algiers? °C
(d) Athens and Oslo? °C
2. Find two cities that have…
(a) temperatures the same number of degrees from 0°C and
(b) a temperature difference of 11°C. and
Try this!
1. What number is missing at the arrow?
I think this one is zero. What do you think?
2. What number is halfway between 8 and –4?
Adding and Subtracting Positive and Negative Numbers 1
Use a number line of your choosing to model and solve these.
You could use an arrow and number line in your copy
In your copy, express each of these as an expression and solve. Use a number line of your choosing to help you.
For example, the expression for number 1 is 5 – 6.
Use a number line of your choosing to complete these. Then, in your copy, write an equation to show what is happening in each (the function rule).
Let’s talk!
Can you think of a way to calculate , or above without using a number line? If so, explain how.
Try this!
1. A delivery person entered a high-rise building on the ground floor She went up five floors, down eight floors, and then up four floors. On what floor was she then? floor
2. Dean was overdrawn by €25 in the bank. He lodged €40, and then he withdrew €20. What was his balance then? €
Adding and Subtracting Positive and Negative Numbers 2
What value does each set of tiles represent?
Remember: each +1 and –1 form a zero pair, and cancel each other out.
The value of one of the sets of tiles in above was zero. Draw three more sets of tiles, each with a value of zero.
Use positive and negative tiles to model and solve these.
D Use positive and negative tiles to model and solve these.
1. A diver dived down to 10m below sea level. She swam upwards for 6m, and then dived down another 5m. At what depth below sea level was she then? m
2. The temperature at 8 am was 3°C By 2pm it had risen 8 degrees. What was the temperature then? °C
3. A golfer’s score over four rounds was 4 under par, 1 under par, 3 over par and 2 under par What was his final score relative to par?
Try this!
1. Use positive and negative tiles to show each number below. Record how you did it. Number to showTiles to use How did you do it?
0four
2six
2. Can 5 be represented using six tiles? Why or why not?
Multiplying Positive and Negative Numbers
Write the matching multiplication sentence for each of these and solve.
Model and solve these. Express the answers as a positive or negative number.
1. A hot-air balloon is losing 5m of altitude every minute. If this continues for 4 minutes, what is the total change in the balloon’s altitude? m
2. A town’s population has been increasing by approximately 100 people per year for the past 6 years. What is the change in population from 6 years ago to today?
3. A team played 9 soccer games. If their mean (average) goal difference for each game was –2, what was the total goal difference for all 9 games?
4. To train for a marathon, Jenna increases her distance by 3km every week. After 6 weeks, what is the total change in the distance she can run? m
5. In the summer, the water level of a tank drops by 2cm every day. What is the total change in the water level after 5 days? cm
Try this!
1. What are the missing values at A and B on this number line? A B
2. Write a multiplication sentence to represent 6 jumps back on this number line.
Divisibility
Complete the table. ✓ or
✗.
Is the number divisible by…2?3?4?5?6?8?9?10?
1. 72
2. 147
3. 816
4. 905
5. 4,320
6. 3,024
7. 36,108
Let’s talk!
What strategies did you use to complete ?
One strategy is to look at the digit in the ones place to identify if the number is divisible by 2, 5 or 10.
Can divisibility be identified without having to use division? Explain how.
Are these always (A), sometimes (S) or never (N) true?
1. If a number is divisible by 9, it is divisible by 3.
2. If a number is divisible by 3, it is also divisible by 6.
3. If a number ends in 2, 4, 6, 8 or 0, it is divisible by 4.
4. If a number is divisible by both 2 and 4, it is divisible by 8.
5. A number is divisible by 3 if the sum of its digits is 15.
Try this!
1. Mystery numbers! Read the clues and work out the possible digits.
(a)
I’m thinking of a 3-digit number: 7 ? 8. I know that it’s divisible by 6.
(b)
I’m thinking of a 4-digit number: 2,1 ? 4. I know that it’s divisible by 4 and 3.
(c)
I added together the digits in the numbers to get the digit sum.
I’m thinking of a 4-digit number: 7, ? 28. I know that it’s divisible by 3, but not by 9.
What are the four possible digits that could go in the box?
What are the two possible digits that could go in the box?
What are the two possible digits that could go in the box?
2. Create your own 4-digit mystery number that is divisible by 2, 5 and 10.
Prime and Composite Numbers
Prime number: a number that has exactly two factors – itself and 1.
Build it! Sketch it! Write it!
Composite number: a number with more than two factors.
Which number is neither prime nor composite?
123
Using your own choice of strategy, identify and list:
1. All of the composite numbers < 20:
2. All of the prime numbers < 20:
Are these always (A), sometimes (S) or never (N) true?
1. The number 1 is the smallest prime number
2. If you add two different prime numbers, the total is a composite number.
3. Prime numbers are also odd numbers.
4. Numbers that end in 7 are prime numbers.
5. There is a prime number before and after every multiple of 6 up to 100.
Find two different prime numbers to answer each clue.
1. The sum of these prime numbers is 10, and their product is 21. and
2. Their difference between these prime numbers is 1. and
3. The sum of these prime numbers is 20, and each is between 5 and 15. and
4. The total of these prime numbers is 30, and each is less than 18. and
D Look at the number on Dara's mini-whiteboard and answer the questions below.
1. True or false? This number
(a) is a composite number.
(b) is a multiple of 3.
(c) is divisible by 4.
(d) is divisible by 9.
(e) when divided by 5, leaves a remainder of 3.
8,357,412
Divisibility tests could be used to help here.
2. Express the number as a decimal number rounded to the nearest tenth of a million.
Try this!
Copy this net of a cube. Write one of the numbers 1, 2, 3, 4, 5, 6 on each face in such a way that, when folded, the numbers on opposite faces add up to a prime number that is not 7.
If needed, you could use PCM XX to help you with this.
Build it! Sketch it! Write it!
Factorisation
Use your own preferred strategy to identify all of the factor pairs for each of these numbers: 24 45 56
Use factors to make these calculations simpler, and solve them.
In above, many of the numbers could have been factorised in multiple ways. What factors did you choose to use and why?
D Complete the branching to find the prime factors. 1. 2. 3.
In your copy, use branching to find the prime factors of: 20 36
Try this! Use factors to help simplify and solve these.
1. A farmer has 684 eggs to be placed in boxes of 18. How many boxes will she need?
2. An airline transports an average of 1,850 passengers every day. What would be the average number of passengers per fortnight (14 days)?
3. A builder needs to lay 72 square tiles in a rectangular room. (a) List all of the possible dimensions (length by width) the room could have, assuming that the tiles are whole. (b) Of the possible dimensions, which are the least likely? Explain why.
Highest Common Factor
The highest common factor (HCF) is the highest (largest) factor common to two or more numbers.
Identify the HCF of each set for numbers.
1. Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
HCF:
Do you remember how to use prime factors to identify the HCF?
2. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
HCF:
Build it! Sketch it! Write it!
Use your own preferred strategy to work out the HCF for these.
1. 18 and 24 2. 27 and 36 3. 26 and 39 4. 56 and 84
Model and solve these.
1. 45 children and 18 adults are on a trip to the zoo They need to be divided into groups with the same number of children and adults in each.
(a) What are the possibilities?
(b) What is the greatest number of groups that can be made?
2. 90 6th Class pupils and 75 5th Class pupils are being organised into groups for a scavenger hunt. What is the greatest number of groups that can be made, ensuring that the ratio of 6th Class to 5th Class pupils is the same in each group?
D Let’s investigate!
Look at Jay. Investigate if what he says is correct by listing all of the factors of the numbers from 2 to 10.
Try this! Which of the numbers below is a common factor of 168 and 217?
2, 3, 4, 5, 6, 7, 8, 9, 10
Explain how you worked it out.
When listing factors of a number, there will always be an even number of factors, because factors come in pairs.
I'll use the divisibility tests for these numbers. I’ll use branching to identify all of the factors.
Lowest Common Multiple
The lowest common multiple (LCM) is the lowest (smallest) multiple common to two or more numbers.
Do you remember how to use prime factors to identify the LCM?
Use prime factorisation to identify the LCM of each set of numbers.
Let’s talk!
Use another strategy to identify the LCM of one of the pairs of numbers in above
Which strategy was most efficient? Explain your reasoning If the starting numbers were 10 or less, would that affect the efficiency of the strategies? Explain your reasoning.
Build it! Sketch it! Write it!
Choose your own preferred strategy to work out the LCM for these.
1. 18 and 24
26 and 39
D Let’s investigate!
Look at Mia. Investigate if what she says is correct by identifying the LCM of various pairs of numbers from 2 to 10.
27 and 35
56 and 84
The easiest way to identify the LCM of two numbers is to multiply them by each other
Write two numbers in each section of the Carroll diagram below.
Factor of 100
Not a factor of 100
Which section can have no more than two numbers in it?
Prime number
Not a prime number
Use your understanding of LCM or HCF to help solve these.
1. A red light blinks every 8 seconds, and a green light blinks every 10 seconds. If they both blink at the exact same moment, how many seconds will pass until they blink together again? secs
2. Mark and David are running laps around a track. Mark completes a lap in 3 minutes, and David completes a lap in 4 minutes. If they both start at the same line at the same time, how long will it take before they cross the starting line together again? mins
3. Lexi has 36 orange balloons and 54 blue balloons. She wants to make identical party bags with the same number of each colour balloon in each bag. What is the greatest number of party bags she can make?
4. A length of yellow ribbon is 96cm long, and a length of green ribbon is 1.2m long If they are both to be cut into pieces of equal length, without any waste, what is the greatest possible length for the pieces? cm
5. A factory machine needs maintenance every 10 hours. Another machine needs maintenance every 15 hours. Both were maintained at 9 a.m. on Monday. At what time and day of the week will both be maintained again at the same time?
6. Aaron visits the library every 6 days, and Kelly visits the library every 8 days. If they both visit the library on the 2nd of the month, on what date will they both visit the library again?
Try this!
1. Find two numbers that share the common multiples of 60 and 75. and
2. Find two numbers that share the common factors of 5 and 9. and
3. Copy this net of a cube. Write one of the numbers 1, 2, 3, 4, 5, 6 on each face in such a way that, when folded, the numbers on opposite faces add up to a factor of 36.
If needed, you could use PCM XX to help you with this.
Square and Cube Numbers
Represent each of these images (a) as an equation and (b) in exponential form.
The smallest number that is both a square number and a cube number is 64. I know that 52 is 25, so 502 must be 250. The square root of 16 is the number that is squared to make 16. Representing values in this way is called exponential form. 23 4 2 × 2 × 2 = 8
Solve these.
Identify the missing number in each of these.
Let’s talk!
Look at Jay and Mia. What do you think? Explain your reasoning
Are these always (A), sometimes (S) or never (N) true?
1. When you square an even number, the result is divisible by 4.
2. A square number has an even number of factors.
3. All square numbers less than 100 can be found by adding two primes together
4. Square numbers are one more than a multiple of 4.
Sort each number in the list into its correct place in the Carroll diagram. 1, 2, 3, 4, 6, 8, 9, 10, 15, 16, 25, 27, 36, 46, 49, 64, 96, 125
(a) Cube number (b) Not a cube number
1. Square number
2. Not a square number
Sort each number in the list into its correct place in the Venn diagram. 1, 2, 8, 16, 19, 36, 27, 64, 67, 91, 100, 125
Cube numbers Even numbers Prime numbers
Try this!
1. Last year, Tim’s age was a square number Next year, his age will be a cube number.
(a) What age is Tim now?
(b) How long until his age is both a square and a cube number? years
3. Look at Lexi. Find two possible numbers that work. and
When I add two numbers, I get a prime number When I multiply them, I get a square number.
2. Look at Mia and Jay. What is the difference between their answers?
I’ve worked out the value of 62 .
I’ve worked out the value of 63
4. Dara made the shape below. How many more small cubes does he need to add so that it represents 73?
More Exponential Numbers
Write these multiplication expressions in exponential form (using indices).
Use your calculator, if necessary, to find the value of each of these.
64 =
83 =
31 =
56 =
94 =
24 =
Without using a calculator, complete this table.
45 =
76 =
13 =
form (a) Value (standard form) (b) Exponential form
1. 10 × 10 × 10 1,000 103
2. 10 × 10
3. 10 × 10 × 10 × 10
4. 10 × 10 × 10 × 10 × 10 × 10
5. 10 × 10 × 10 × 10 × 10
Let’s talk!
The values in above are often described as the powers of ten. Why do you think this is so? What pattern(s) do you notice among the powers of ten?
Write the answers to these in (a) standard and (b) exponential form.
1. On a branch of a tree, there are 5 twigs. On each twig there are 5 leaves. In total, how may leaves are there altogether? (a) (b)
2. In question 1 above, there are 5 ladybirds on each leaf. How many ladybirds are there altogether? (a) (b)
3. On a street, there are 4 houses. In each house, there are 4 rooms. In each room, there are 4 chairs. How many chairs are there altogether? (a) (b)
4. In question 3 above, on each chair there are 4 legs. How many legs are there altogether? (a) (b)
Model and solve these.
1. The number of lily pads growing in a pond doubled each day until day 10, when the entire pond was covered with lily pads. On what day was half of the pond covered? Day
2. A population of bacteria that was growing in a Petri dish doubled every 20 minutes. On day 3 at 4:00 p.m., the Petri dish was completely full of bacteria. At what time of the day was the Petri dish exactly…
(a) half full? : (b) quarter full? :
G Let’s investigate!
Which would you rather?
For doing chores at home, your parents have offered you the following payment options:
● Option A: Receive €1 every day for 14 days.
● Option B: Receive 1c on day 1, and on every subsequent day, you receive double what you received on the previous day.
Use the grids to work out which option is better, and answer the questions below.
Option B
1. If the offer is only for 14 days, which option should you choose? Option
2. If the offer is only for 10 days, which option should you choose? Option
3. Justify your reasoning with mathematical proof.
Try this!
1. Complete this table. What pattern(s) do you notice?
Hint: Look at the indices. Option A
2. Solve these without writing them in expanded form. (a) 76 × 72 = 7 (b) 85 × 85 = (c) 64 × 63 = (d) 102 × 10 = 105
Multiplying and Dividing by Powers of Ten
If multiplying, move the digits to the left. If dividing, move the digits to the right.
Calculate these.
1. 8 149 × 10 =
2. 27.4 ÷ 100 =
3. 1,000 × 3,986 =
4. 4 7 ÷ 10 =
5. 100 × 32.4 = 6. 48,459 ÷ 1,000 =
Tip! The number of zeros tells you how many places to move the digits.
D Use the moving digits strategy to convert these units of measurement.
Think about how many of the smaller units there are in the larger unit. Then, if converting from the smaller unit to the larger unit, divide by that number
And if converting from the larger unit to the smaller unit, multiply by that number
1. 2,548c = € 2. 1,983cm = m 3. 2.34l = ml 4. 35m = km 5. 23,458ml = l 6. 32,671g = kg
7. 0 203m = mm 8. 0 046km = m 9. 3cm = m 10. €508 = c 11. 26ml = l 12. 0.15kg = g 13. 108mm = cm 14. 74,545c = € 15. 6g = kg
Try this!
1. The distance around a walking track is 908m. What is the distance of 10 laps of the track in kilometres? km
2. The weight of jam in a jar is 0 45kg. What is the weight of jam in 100 of these jars in grams? g
3. The length of a crayon is 95mm. What would be the total length in metres of a line of 1,000 such crayons laid end to end? m
Multiplying and Dividing by Multiples of Powers of Ten
Complete these and solve. 1. 20 × 300 = 2. 2,400 ÷ 600 = 3. 63,000 ÷ 700 =
16 × 400 =
45,000 ÷ 500 =
Simplify and solve these calculations using your own preferred approach.
Find the missing multiplier. Check your answer using substitution. 1. 0 8 × =
Let’s talk!
Look at the calculations below. Which ones do not look correct? Explain your reasoning. Now, check them with a calculator.
D In your copy, use the column method to solve the incorrect calculations in above.
Let’s talk!
Estimate a reasonable answer for each of the calculations in below. Explain your strategy. Solve these.
Use your calculator to check the answers to D and without using the × .
Try this! Choose your own strategy to answer each of these.
1. Mike’s car travels 14 34km per litre of petrol on the open road, and 10 65km per litre when driving in the city. How far should it travel using 9 5 litres on…
(a) a motorway? km
(b) city streets? km
2. A bucket held 8 46l of water. If it took nine and a half of these buckets to fill a tank, what was the capacity of the tank? l
3. As part of a restoration project, 16.62 million trees were planted in a forest. The following year, 4 9 times as many trees were planted. How many trees were planted the following year? million
4. The population of Zimbabwe is 17.26 million. Germany’s population is 4 8 times that number What is the population of Germany? million
5. Calculate the area of a tennis court if the length is 23 77m and the width is 8.2m. m2
6. An electricity supplier offered a discounted electricity rate of 9·6c per unit used. If, on average, 102·6 units per week are used, what is the average cost of usage per week in…
(a) cent? c
(b) euro rounded to the nearest cent? €
H Let’s play!
Number of players: 2–6
Chance Calculations – Multiplication with Decimals
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● To start, on their mini-whiteboard, each player draws these boxes for a multiplication calculation.
● Each player, in turn, spins the spinner and writes the number spun into one of their boxes. When all of the boxes are full, each player calculates their product.
● The player with the highest product wins.
Variation
● Play as above, but this time the player with the lowest product wins.
Mixed Operations
Maths Choice Board: Choose 3 of these tasks to explore and solve. Present your solutions in different ways.
Gaelic Games
A school principal bought 28 new hurleys costing €16.25 each.
1. What was the total cost of the hurleys?
2. What change did the principal have from €500?
Fuel Pump Maths
If diesel costs 124 9c/litre, how much will it cost for 8 5 litr of diesel in…
1. cent?
2. euro?
Lift Off?
The principal of a 2-storey school plans to buy a laptop trolley with 16 laptops and charger packs. He needs to be able to bring it up to the first floor in the lift. Using the information below and your own evidence, explain whether you think this can be done or not.
● Weight of each laptop: 2.448kg
● Weight of each charger pack: 0.375kg
● Weight of trolley: 92kg
● Maximum load in lift: 500kg
Fluffy Flooring
What is the cost of carpeting a room that is 2.6m wide and 3.5m long if the cost of the carpet is €26 50 per square metre?
Apples for Sale
What is the cost of 1 7kg of apples that cost €2 40 per kg?
Whitney’s Wages
Whitney earns €751 46 gross per week. From this, deductions totalling €164 74 are taken.
1. What is Whitney’s net (take-home) pay each week?
2. For a period of 26 eks, calculate her total… (a) gross pay (b) deductions (c) net pay
1. How much would it cost for a bracelet and 4 heart charms?
2. If it costs €21 10 for a bracelet, 3 heart charms and 2 flower charms, how much does a flower charm cost?
3. If it costs €30 20 for a bracelet, 4 flower charms and 3 bee charms, how much does a bee charm cost?
Make Your Own Charm Bracelet
Measuring Angles
Let’s talk!
Look at each angle in below. Say what type of angle each one is. How could you measure each angle?
For some of these angles I think I will need to use the protractor twice and then add the two measures.
For some of these, I could measure the degrees in the smaller inner angle, and then subtract that from 360.
Estimate (E) and then measure (M) the degrees in each angle.
Answer these.
Mia is thinking of a way to estimate and sketch a 45° angle without measuring it.
I know that the angle in a square is 90°. 45 is half of 90, so a 45° angle is half the size of the angle in a square
Think of ways to estimate these target angles compared to other angles that you know, and sketch your estimates in your copy. 1. 135° 2. 225° 3. 30°
350°
D Measure the angles that you sketched in above. Calculate the difference between your measurement and the target angle for each.
Target angle (a) Measure of sketch (b) Difference
Let’s talk!
Which of the angles in above did you find easiest to estimate? Which did you find hardest?
Let’s talk!
Defining Shapes
Look at the children. Who is right? What other shapes could Lexi be thinking of?
I’m thinking of a 4-sided shape with 2 pairs of parallel sides.
It could also be a parallelogram. It’s a rectangle!
Write the letter for each shape in the correct section(s) of the table below.
AB CD EF GH
1. Polygon: A, B, C, D, E, F, G, H
3. Parallelogram:
5. Rhombus:
7. Trapezium:
2. Quadrilateral:
4. Rectangle:
6. Triangle:
8. Kite:
Look at your answers to above and answer these.
1. Which shape (by letter) appears in the most sections of the table?
2. Which shapes (by letters) appear in the fewest sections of the table?
3. Which section of the table has the most shapes in it?
4. Which sections of the table have the fewest shapes in them?
D In your copy, write a minimal defining list for each of the sections in above.
Are these always (A), sometimes (S) or never (N) true?
1. A triangle is a polygon.
2. A pentagon is a quadrilateral.
3. A square is a parallelogram. 4. A parallelogram is a rectangle.
F Maths eyes
What shapes can you see?
A minimal defining list is the smallest possible list of properties that define a shape uniquely.
Write all of the possible shape names for each.
1. 2.
1.
2.
Angles Around Lines
Look at the diagram. Colour all of the angles (or first trace the diagram into your copy) that are the same size as…
1. angle A, red
2. angle B, blue
This diagram shows 2 pairs of parallel lines and the angles they form.
Look at the angles in above and complete the table.
Angle (a) Estimate (b) Measure (c) Difference
A
B
Let’s talk!
I chose one red angle and one blue angle in and found the sum.
Look at Jay. What do you think was the sum of his angles? Explain why. If you choose any red angle and any blue angle in , would the sum be the same?
D Work out the size of the angle marked with a question mark in these.
Two angles that add up to 180° are called supplementary angles.
The matching arrows in numbers 3 and 4 mean the lines are parallel.
Try this! Use what you know about angles to work out if each pair of lines is parallel or not. ✓ or
Angles in a Triangle
Draw a triangle in your copy. Measure and label the angles.
1. What do the angles add up to?
2. Do the same for another triangle. What do the angles add up to?
Work out the missing angle in each triangle.
Estimate the size of angle C in each triangle.
Estimate of C: °
Estimate of C: °
D For the triangles in above, calculate the size of angles A, B and C.
E Let’s investigate! Interior and exterior angles in a triangle.
1 Measure the angles and complete the table.
An interior angle is inside the triangle. An exterior angle is outside the triangle, and it makes a straight line with an interior angle.
2. In your copy, draw three different triangles. Label the interior angles A, B and C, and the exterior angles X, Y and Z. Measure the angles and make a table like the one above for each of your triangles.
3. What do you notice about the angles in the tables? Can you explain why?
Angles in Polygons
Draw a quadrilateral in your copy. Measure and label the angles.
1. What do the angles add up to?
2. Do the same for another quadrilateral. What do the angles add up to?
Use what you know about the angles in quadrilaterals to find the missing angle in each trapezium.
Remember: If an angle is marked with a small square, that means it’s a right angle.
Let’s talk!
In each trapezium in above, add the two angles on the left-hand side. Next, add the two angles on the right-hand side. What do you notice? Why do you think this is so?
D If a quadrilateral has angles of 100° and 80°, what could the other two angles be? Find three possible answers.
1. ° and ° 2. ° and ° 3. ° and °
Let’s talk!
Do you agree with Mia? Explain why.
I think the quadrilateral in D above must have a pair of parallel sides.
Work out the missing angle(s) in each irregular quadrilateral.
Hint: The total of angles in a quadrilateral will be _____degrees.
Find two different ways to divide a regular hexagon into four triangles.
Work out the sum of the angles in a…
To find the sum of the angles, subtract 2 from the number of sides, and multiply the answer by 180°.
Use your answers for above to work out the size of an interior angle in a…
In a regular polygon, all of the interior angles are the same size.
Try this! Write a set of possible angles for each of these shapes.
Constructing Shapes
In your copy, use a ruler and a pair of compasses to construct triangles with these side lengths.
What type of triangle did you construct for each part of above?
In your copy, use a ruler and a protractor to construct these shapes to scale.
D Calculate the size of each of the missing angles in above. Then, measure to see if your calculations were correct. Did you get the right answer? ✓ or ✗.
°
°
°
Let’s talk!
Why do you not need to know all of the side lengths and angles to be able to construct a quadrilateral?
Discuss as a class or in groups.
F Let’s investigate!
1. Choose three lengths of between 1cm and 10cm.
2. Try to construct a triangle with your chosen lengths.
3. Investigate if it will work for any three lengths.
4. Can you find a rule to describe whether or not three lengths can make a triangle?
Build it! Sketch it! Write it!
I will use materials to construct these.
I will sketch them.
1. Construct two different triangles whose sides add up to 12cm.
2. Construct two different isosceles triangles whose sides add up to 20cm. I’ve put my results in this table.
I will use an app to model these.
Circle Relationships
Let’s talk!
Look at the circle and look at the children. Why, do you think, did the children get different answers for the circumference?
I think the circumference of the circle is 18cm.
3cm
I think it’s 18 6cm.
Use a calculator to calculate the circumference of each circle.
I think it’s 18.84cm.
To calculate the circumference, multiply the diameter by π. π = 3.14
These circles haven’t been drawn to scale so you will need to work out your answers.
Follow these steps to construct a sector of a circle in your copy.
1. Draw a line 5cm long
2. From one end of your line, measure an angle of 60°. Draw a line of 5cm at this angle.
3. Put the point of your compass at the place where the two lines meet, and the pencil at the other end of one of the lines. Draw an arc joining the two lines.
Let’s talk!
What was the angle in your sector in above?
Look at Lexi and Jay. Why, do you think, did they get different angles?
The angle in my sector was 60°. The angle in my sector was 300°.
In your copy, construct a sector with a…
1. radius of 6cm and an angle of 90°
3. radius of 5cm and an angle of 270°
radius of 4cm and an angle of 120°
Try this! Calculate the arc length of each sector in above Use a value of 3·14 for π
The Area of a Circle
Look at the circles and answer the questions below.
1. Write the radius.
2. Find the area of the small square. A cm2
3. Find the area of the large square.
4. Estimate the area of the circle by counting squares. Estimates:
Let’s talk!
Compare the area of the small square with the area of the large square. Compare the area of the circle with the small square and the area of the circle with the large circle. What do you notice?
I think the area of the circle is about 3 and a bit times the area of the small square.
That reminds me of a special number in maths.
What is the special maths number that you have encountered before?
Use a calculator to find the area of each circle in above using a value of 3·14 for π.
D Use a calculator to complete the table. Use a value of 3·14 for π.
1. Area
2. Curved circumference
3. Straight perimeter
4. Total perimeter
Teacher’s Planning Book Extract Contents
The Maths and Me Teacher’s Pack contains a Teacher’s Planning Book and a Teacher’s Resources Book. Along with the plans for each unit, the Teacher’s Planning Book also contains a comprehensive introductory section featuring the following sections:
● How Maths and Me Aligns to the Primary Maths Curriculum
● Your Guide to Maths and Me
● Supporting Maths Learning in Your Classroom
● Yearly Overview
The Maths and Me Teacher’s Resources Book includes all additional materials outside of planning. A range of photocopiable materials (PCMs) will be available, including general PCMs. For each unit the following are provided:
● Let’s Strengthen PCMs
● Let’s Deepen PCMs
● Let’s Strengthen Suggestions for Teachers
● Maths Journal Prompts PCMs
● Home/School Links PCMs
● Games Bank
Additionally an Answer Booklet and various printables (such as manipulative printables, Maths Language Lists and Equipment List) are also available.
Str and(s) > Str and Unit(s) Number > Place Va lue and Base Te n; Fr actions.
Experiences Assessment
Intuitiv e Assessment: re sponding to emer ging misconceptions
D Concept Car toon L1, 5 D Think -P air -Shar e L1, 3–6 C D Re ason & Re spond L1–4, 6 C D Wr ite-Hide-Sho w L1–4, 6 C Build it; Sk etch it; Wr ite it L1
Re ading, Comparing and Ordering Numbers L1
Planned Inter actions: re sponding to insights gleaned fr om childr en’ s re sponses to learning experiences Assessment Ev ents: inf ormation gather ed fr om completion of the unit assessment in the Pr ogr ess Assessment Booklet page XX
Ke y: Elements: (U&C ) Understanding and Connecting; (C ) Communicating; (R) Re asoning; (A&PS) Applying and Pr oblem-Solving. CM: Cuntas Míosúil: please tick when yo u ha ve completed the fo cus of learning. Learning Experiences: C concr ete activity; D digital activity; P activity based on printed materials, fo llo we d by lesson numbers. Maths and Me : 6th Class –Shor tTe rm Plan, Unit 1: Place Va lue (September: We eks 1&2)
Outcome
Learning
( s )T hr ough appr opriately pla yful and engaging learning experiences childr en should be able to in ve stigate ho w decimals and per centages (and fr actions) can be compar ed, order ed and expr essed in re lated terms; explor e (model, compar e and con ve rt ) the re lationships betw een fr actions, decimals and per centages; in ve stigate pr opor tionality and ra tios of quantities (sets). Lesson Fo cus of Learning (with Elements)
1 Place Va lue: Identifies and gener alises ho w place value wo rks [the value of each digit and the value of the entir e number] (R); Explor es the idea that the po we rs of base ten continue infinitely (U&C )
2 Decimal Numbers: Re cognises and uses thousandths and re lates them to tenths, hundr edths and decimal equivalents (U&C )
3 Millions: Extends pr evious conceptual and pr actical wo rk to include lar ger numbers (U&C )
Thr eeAct Ta sk L5 Print re sour ces Pupil’ s Book pages 6–1 4 PCM XX
4 Estimating and Ro unding Numbers: Uses their skills of ro unding and estimating (R)
5 Po sitiv e and Negativ e Numbers: Identifies positiv e and negativ e numbers in context (U&C )
6 Po sitiv e and Negativ e Numbers on the Number Line: Re cognises negativ e numbers and extends re gular patterns that include negativ e numbers (R)
Additional information for planning
Progression Continua
Maths Language
Equipment
Inclusive Practices
Integration
Home/School Links
See ‘6th Class Maths and Me Progression Continua Overview’ for a detailed breakdown of how all progression continua are covered.
See ‘6th Class Maths and Me Maths Language Overview’ (Appendix 2), individual lesson plans and Unit 1 Maths Language Cards.
See ‘6th Class Maths and Me Maths Equipment Overview’ (Appendix 3) and individual lesson plans.
● See Let’s Strengthen and Let’s Deepen suggestions throughout lesson plans.
● See Unit 1 Let’s Strengthen Suggestions for Teachers. (These address the Common Misconceptions and Difficulties listed below.)
● See Unit 1 Let’s Strengthen PCM.
● See Unit 1 Let’s Deepen PCM.
See individual lesson plans.
See the Unit 1 Home/School Links PCM and Pupil/Parent App.
Background and rationale
● This unit is a two-week block of content incorporating whole number and decimal number learning experiences (see progression continua levels j and k) from the strand units of Place Value and Base Ten, and Fractions. Its purpose is to review and further develop the children’s understanding of the base ten number system, including that it extends infinitely in both directions.
● The final lesson in this unit reviews the children’s understanding of positive and negative numbers (introduced in 5th Class), and lays the groundwork for operations involving positive and negative numbers in Unit 2 Operations 1. While negative numbers might seem like a separate concept, there is a strong rationale for including them as part of a unit of work on place value, which is fundamentally about understanding the structure of the number system and the relative value of digits. Introducing negative numbers expands the number line beyond zero, showing the children that numbers extend infinitely in both directions. This reinforces the idea that numbers have both magnitude (size) and direction (positive or negative).
● In keeping with the new PMC 2023, Maths and Me uses the terminology of ‘tens and ones’ as opposed to ‘tens and units’. That said, it would be beneficial to explicitly explain that the terms ‘units’ and ‘ones’ are interchangeable, especially as the children may encounter ‘units’ elsewhere.
● As was emphasised in Maths and Me for 3rd Class and 4th Class, the children should be encouraged from the beginning to use both decimal language and fractional language when verbalising decimal notation (i.e. expressing 7.185 as ‘seven point one eight five’ and also as ‘seven and 185 thousandths’). Using fractional language to read decimals in this way reinforces the value of the digit(s) in the decimal place(s).
● The children should be encouraged to model and express values in multiple ways in order to reinforce their understanding of the connections between equivalent forms, for example: 0.125 = 125 thousandths ( 125 1,000 ) = 1 tenth, 2 hundredths and 5 thousandths ( 1 10 + 2 100 + 5 1,000 ).
Common misconceptions and difficulties
● The children may have difficulty understanding the base ten system and/or grasping its infinite nature.
● They may have trouble comprehending the scale of millions, and struggle to relate them to realworld quantities.
● They may incorrectly assume that thousandths are bigger than hundredths (i.e. struggle with the inverse relationship between the size of the decimal place value and its magnitude).
● They may not appreciate that a zero can be unnecessary (e.g. at the front of a whole number or the end of a decimal number), or that it can be a necessary placeholder in the middle of a number.
● They may incorrectly read, write and/or represent numbers (e.g. demonstrate incorrect usage of the comma as a digit separator; read 7.38 as ‘seven point thirty-eight’, or 2.12 as ‘two and one twelfth’; not realise that one-tenth can be written as 0.1, .1, 0.10, 0.100, and so on). Expressing decimals in a variety of equivalent forms can help reinforce children’s understanding of their equivalency, including the role of zero
● They may incorrectly assume that a number with more digits is always greater, regardless of place value (e.g. thinking that 12.34 is bigger than 999).
● They may have trouble grasping the concept of numbers less than zero, as they may not have real-world experience with them. They may also incorrectly assume that the bigger the negative number, the larger the value (e.g. that –10 is greater than –5 because 10 is bigger than 5).
The Unit 1 Let’s Strengthen Suggestions for Teachers address the common misconceptions and difficulties listed above.
Mathematical models and representations
● Number lines
● Tenths, hundredths and thousandths grids
● Place value grids
● Place value counters
● Base ten blocks
● Base ten money
● Thermometers
Teaching tip
The following manipulative printables are available to support the unit: Open Number Lines, Hundredths Grid, Thousandths Grid, Place Value Grid, Place Value Counters, Base Ten Blocks, Base Ten Money Click on the resources icon on the Maths and Me book cover on edcolearning.ie
Days 1 and 2, Lesson 1
Place Value
● Explores the idea that the powers of base ten continue infinitely (U&C) Focus of learning (with Elements)
● Identifies and generalises how place value works [the value of each digit and the value of the entire number] (R)
Digital activity: Do We Have a Base Ten System?
MAM Routines: Concept Cartoon, with Think-Pair-Share
Concrete activity: How Much is Here? MAM Routines: Reason & Respond, with Write-Hide-Show
Video: The Place Value System
MAM Routines: Reason & Respond, with Write-Hide-Show
Concrete activity: Zero as a Placeholder
MAM Routine: Build it; Sketch it; Write it
Concrete activity: Reading, Comparing and Ordering Numbers
Pupil’s Book pages 6–7: Place Value
Maths language
● ones, tens, hundreds, thousands, millions, place value, base ten system, digit, decimal (point), comma (digit group separator), unnecessary/necessary zero, placeholder, compare, order, greater than (>), less than (<)
Teaching tip
This lesson explores the core ideas of our base ten place value system: the ten-times relationship between places; the role of decimals; the significance of commas as digit-group separators and of zero as a placeholder.
Warm-up
Do one of these warm-up activities on each day.
D Digital activity: Do We Have a Base Ten System?
MAM Routines: Concept Cartoon, with Think-Pair-Share
Display the Concept Cartoon, in which the characters are looking at a place value grid and discussing whether our number system should be called a ‘base ten system’. Click to hear each character’s thoughts. Then, using Think-Pair-Share, ask:
● What do you think?
● (Point to a specific character.) Do you agree with their idea? Explain why.
● Do you think something different? What do you think? Why do you think this?
If appropriate, record the children’s responses to these questions on the board. Allow the children the opportunity to respond to (agree/disagree with or query) others’ responses, but do not confirm or reject any of the ideas. Afterwards, ask/say:
● Does our number system only go up to thousands?
● What group is bigger than the thousands group? And what is bigger than that?
● I wonder if it is just a coincidence that individual numbers are called digits and fingers are also called digits, and that ten is an important part of our number system and we have ten fingers. What do you think?
Teaching tip
The most likely reason for the origin of our base ten system is that humans have ten fingers. When early humans needed to count things like animals, tools or people, they naturally used their fingers. Each finger represented one, and since we have ten fingers, it was logical to group things in sets of ten.
Let’s deepen
Challenge the children to give other examples of number systems we use that are based on ten (e.g. metric measures), and those that are not (e.g. imperial measures, time).
C Concrete activity: How Much is Here?
MAM Routines: Reason & Respond, with Write-Hide-Show
Write a random number on the board. As appropriate to the ability of the class, the number chosen can be a whole number only up to and including millions (not beyond 9.9 million), and/or include up to three decimal places.
Teaching tip
Use a 0–9 spinner or an online number generator to create a random number.
Underline a digit, and ask:
● How much is here?
Repeat with the other digits. Encourage the children to express the value of the digit in multiple ways, for example, if the underlined digit is 8 in the tenths place, it could be expressed as 8 tenths ( 8 10 ), 80 hundredths ( 80 100 ) or 800 thousandths ( 800 1,000 ) Repeat as required with other numbers.
Main event
D Video: The Place Value System MAM Routines: Reason & Respond, with Write-Hide-Show
Play the video and, using Write-HideShow, ask the children to respond to the questions on their MWBs, giving reasons for their responses as appropriate.
Let’s deepen
Challenge the children to suggest the name given to the values that come to the right of thousandths (ten thousandths, hundred thousandths, millionths, etc.).
C Concrete activity: Zero as a Placeholder MAM Routine: Build it; Sketch it; Write it
Distribute PCM xx Place Value Grid. Write the number 3.5 on the board, and using Build it; Sketch it; Write it, ask the children to model the number:
● Build it! Use any classroom resources to represent the number (e.g. with base ten money – three €1 coins and five 10c coins, or with straws – three whole straws and five cut-up tenths).
● Sketch it! Draw area models (e.g. circles, rectangles, squares), linear models (e.g. bar models, open number line on the children’s MWBs).
● Write it! Place it on a place value grid (PCM xx), recording it as 3 ones and 5 tenths.
To promote discussion, ask/say:
● Does it change the value of this number, or its model, if a zero is inserted after the digit 5? Explain why. (No, because it is unnecessary; at the end of a decimal number adding zeros does not change the value.)
● Does it change the value of this number, or its model, if a zero is inserted between the 5 and the decimal point? Explain why. (Yes, because now there are 0 tenths and the 5 has become 5 hundredths.)
● Does it change the value of this number, or its model, if a zero is inserted between the 3 and the decimal point? Explain why. (Yes, because now there are 0 ones and the 3 has become 3 tens or thirty.)
● Does it change the value of this number, or its model, if a zero is inserted before the 3? Explain why. (No, because it is unnecessary; at the front of a whole number adding zeros does not change the value.)
● What can you say about the effect of the zeros? (Zeros make a difference in the middle of a number, i.e. they are necessary zeroes, and act like spacers, keeping the other digits in their correct places. They show that there is nothing in that particular place value.)
C Concrete activity: Reading, Comparing and Ordering Numbers
With the children working together in groups of four, five or six, ask them to write a 6-digit whole number on their MWBs or a piece of paper.
● Reading: Pass the numbers around the group for the children to read each one.
● Comparing: In pairs, both children compare their numbers and write <, > or = to show the relationship.
● Ordering: Lay out the numbers in ascending order (growing) and then descending order (shrinking).
Teaching tip
Maths Journals: The children could record the comparing and ordering phases of this activity, using the appropriate symbols.
Let’s strengthen
The children may benefit from being able to model the numbers as part of this activity. While it is often not efficient or feasible to model larger numbers using physical materials, the Place Value tool in the e-Toolkit could also be used for this purpose. Counters could also be used to model the structure of up to 6-digit numbers, and decimal numbers to 3 places. The counters can also be composed/decomposed.
Teaching tip
When verbalising numbers, ensure the correct word form is spoken (e.g. for the number 32,150, say ‘thirty-two thousand, one hundred and fifty’, rather than ‘three two one five oh’). Encourage all adults supporting the children, including other teachers, assistants and parents, to use the correct word form when reading out numerals. Also, when verbalising the digit zero, say ‘zero’, rather than ‘O’ (O is a letter of the alphabet and therefore not a digit).
Optional consolidation and extension possibilities
Maths Journal Use the Lesson 1 prompt from the Unit 1 Maths Journal Prompts PCM.
Display Set up a display for Place Value in the classroom. This could include examples of the children’s work from this and subsequent units, alongside appropriate labels (see the Unit 1 Maths Language Cards).
Games Bank Play ‘Win Big’ or ‘Less is Best’.
Integration History: Watch this video to learn more about the origins of our base ten number system and other number systems: edco.ie/4due
Maths Eyes The children could research the various ways that numbers are represented in different countries. For example, in most English-speaking countries, commas are typically used as digit-group separators (e.g. 3,000,000), but in many other countries, spaces are used (e.g. 3 000 000). In some European countries, full stops are used (eg. 3.000.000) and a comma is used instead of the decimal point.
How Much Is Here? Working in pairs, one child writes a 6-digit whole number on their MWBs, underlines (or points to) one digit, and asks, ‘How much is here?’ Repeat for each digit in turn. Swap roles for the next number. Variation: Underline two adjoining digits each time.
Digital Online Tools
● This virtual manipulative uses counters to model the structure of up to 7-digit numbers and decimal numbers to 4 places. The counters can also be composed/decomposed: White Rose Place Value Chart at edco.ie/hhae
● This virtual manipulative can be used to model the written structure of whole numbers of up to 7 digits (note that in US English, as used in this resource, the word ‘and’ is not used after ‘hundred’): Toy Theatre Place Value Chart at edco.ie/szs3
Review and Reflect Use the prompt questions in the Review and Reflect Poster.
P Pupil’s Book pages 6–7: Place Value
Days 3 and 4, Lesson 2
Decimal Numbers
Focus of learning (with Elements)
● Recognises and uses thousandths and relates them to tenths, hundredths and decimal equivalents (U&C)
Learning experiences
Digital activity: What Value Does This Represent? (A) and (B)
MAM Routines: Quick Images, with Write-Hide-Show
Video: Decimals
MAM Routines: Reason & Respond, with Write-Hide-Show
Concrete activity: Decimals
Concrete activity: Recording Decimal Numbers on a Place Value
Grid MAM Routine: Write-Hide-Show
Pupil’s Book pages 8–9: Decimal Numbers
Maths language
Warm-up
D Digital activity: What Value Does This Represent? (A) and (B) MAM Routines: Quick Images, with Write-Hide-Show
Teaching tip
While this is a Quick Images resource, because of the nature of detail in the graphics, each image may need to remain on screen for longer
Display the slideshow. Click to briefly reveal and then hide the image on the first slide, which shows a representation of a number. Ask the children to record the value represented on their MWBs, and to ‘show’ their proposed answer when called upon. Record all of the proposed answers on the board, being careful not to give any undue weight to the correct answer. Ask:
● Which answer are you going for?
● What proof do you have?
● Does anybody have different proof?
● Are there any proposed answers that are equivalent forms, representing the same amount or value (‘same value, different appearance’)?
● PCMs xx, xx Equipment
● Reusable dry-erase pockets (if available)
● fraction(s), decimal(s), point, whole, parts, divide, equal, tenth(s), hundredth(s), thousandth(s), standard form, expanded form
Teaching tip
For every image, prompt the children to suggest multiple different ways to write the amount, e.g. 48 hundredths ( 48 100 ) = 4 tenths and 8 hundredths = 4 10 + 8 100 = 0.48 = 0.4 + 0.08.
If any unreasonable answers are suggested, ask:
● Are there any answers that are unreasonable/ unlikely because they don’t make sense? Which ones?
● Why do you think this?
When there are no new strategies to discuss, reveal the image again and confirm the answer using a variety of possible strategies. Repeat for the remaining images.
Teaching tip
For the images showing number lines, ask the children to suggest what the intervals represent and how that could be used to help to identify the missing value.
Main event
D Video: Decimals MAM Routines: Reason & Respond, with Write-Hide-Show
Play the video and, using Write-HideShow, ask the children to respond to the questions on their MWBs, giving reasons for their responses as appropriate.
C Concrete activity: Decimals
Distribute a copy of PCM xx Thousandths Grids to each child. Ask the children to use each grid to represent a random decimal fraction.
Teaching tip
The PCMs could be placed inside reusable dryerase pockets (if available) and used with markers.
The children should colour in the amount and record the values in both fraction and decimal form below the pictorial representation, for example:
● 3 tenths = 3 10 = 30 100 = 300 1,000 = 0.3
● 7 hundredths = 7 100 = 70 1,000 = 0.07
● 365 thousandths = 365 1,000 = 0.365
Teaching tip
Depending on the availability of digital devices, online virtual manipulatives could also be used to model fractions. See the suggestions in the Optional Consolidation and Extension Possibilities section for this lesson.
The following questions could be asked during or after the activity to assess understanding:
● Show me your representation. How do you know you are correct?
● How might you do this in an efficient way? (e.g. for 365 thousandths, instead of colouring in and counting 365 individual parts, instead colour three full rows/columns and 6 hundredth squares, and 5 thousandths/half of 1 hundredth.)
● Does this remind you of any other fraction or decimal? (If not suggested, prompt the children to recognise how each full row/column is also a tenth of the whole shape.)
● What value is represented by the uncoloured parts of the grid? How do you know? Do you need to count all of the uncoloured parts? Explain why.
Let’s deepen
Challenge the children to suggest strategies for identifying the value of the uncoloured amount, and to come up with a way to justify their approach. If not suggested, prompt them to realise that if there are 1,000 thousandths in total, they can use their understanding of bonds of 100 and 1,000 to help identify the uncoloured part.
Teaching tip
Maths Journals: The children could record what they have learned in this lesson, and/or paste in their completed thousandths grids from PCM xx.
C Concrete activity: Recording Decimal Numbers
on a Place Value Grid
MAM Routine: Write-Hide-Show
Teaching tip
Decimals can be written…
● in standard form (e.g. 1.345)
● in expanded form (e.g. 1 + 0.34 + 0.05)
● as an equivalent fraction in standard form (e.g. 1 345 1,000 )
● as an equivalent fraction in expanded form (e.g. 1 + 3 10 + 4 100 + 5 1,000 ).
It is very important that the children recognise this and can change an amount from one form to another
On their MWBs, ask the children to draw a place value grid of:
O. th th
Alternatively, if available, reusable dry-erase pockets and markers could be used with PCM xx Place Value Grid.
Call out a random decimal number (see suggestions below) and, using Write-Hide-Show, ask/say:
● Write and read out this number as a decimal using digits. This is a decimal in standard form.
● What digit is in the tenths (or thousandths/ones/ hundredths) place?
● Which place has the greatest value?
● Which place has the least value?
Unit 1: Place Value
● Write and read out this number as a decimal in expanded form using the plus symbol so that we can see all of the different parts. (This is also called partitioning the decimal into expanded form.)
● In what other way could this number be written?
● Write and read out this number as a fraction using a fraction line (fraction notation). This is a fraction in standard form.
● Write and read out this number as a fraction in expanded form using the plus symbol so that we can see all of the different parts. (This is also called partitioning the fraction into expanded form.)
Suggested numbers:
4 tenths and 7 hundredths 5 hundredths and 1 thousandth 9 tenths, 3 hundredths and 4 thousandths 8 tenths and 6 thousandths
2 (ones) and 3 hundredths 5 (ones) and 2 thousandths
4 (ones) and 13 thousandths 2 tenths, 7 hundredths and 5 thousandths
Let’s strengthen
The children may benefit from using the Unit 1 Let’s Strengthen PCM, which shows some of the equivalent ways in which the same fraction or decimal can be expressed. If the children struggle to identify the value of each digit within the decimal part of the number, encourage them to sketch the number using thousandths grids (see PCM xx).
Optional consolidation and extension possibilities
Maths Journal Use the Lesson 2 prompt from the Unit 1 Maths Journal Prompts PCM.
Display The children could contribute samples of their own work from this lesson and label them.
‘Number of the Day’: Create a 2-D and/or 3-D display for a particular whole or decimal number illustrating all the different ways to represent that number. Each day, a number of significance could be used (e.g. population of a city or country, the asking price of a local house, the distance in km between major cities).
Online Game Play this game, which only goes to tenths, but is quite challenging and provides good reinforcement for visualising where a decimal number is located in relation to another (choosing ‘decimals’): ‘Battleship Numberlines’ at edco.ie/as3v
Digital Online Tools Use these place value tools:
● ‘Decimal Squares’, virtual manipulatives that can be used to model and compare tenths, hundredths and/or thousandths, at: edco.ie/7any
● ‘Number Line’, a tool that can be used to represent decimal numbers to three decimal places, at: edco.ie/uup8
Review and Reflect Use the prompt questions in the Review and Reflect Poster.
P Pupil’s Book page 8–9: Decimal Numbers
Day 5, Lesson 3
Millions
Focus of learning (with Elements)
● Extends previous conceptual and practical work to include larger numbers (U&C)
Learning experiences
Digital activity: Same But Different – Numbers to Millions MAM Routines: Reason & Respond, with Think-Pair-Share
Video: How Big is a Million?
MAM Routines: Reason & Respond, with Write-Hide-Show
Pupil’s Book page 10: Millions
● There is no new maths language for this lesson.
Warm-up
D Digital activity: Same But Different – Numbers to Millions MAM Routines: Reason & Respond, with Think-Pair-Share
● There is no equipment needed for this lesson. Equipment
Play the slideshow and, using Think-Pair-Share, ask the children to propose reasons for why the images are the same and why they are different.
Main event
D Video: How Big is a Million? MAM Routines: Reason & Respond, with Write-Hide-Show
Play the video and, using Write-Hide-Show, ask the children to respond to the questions on their MWBs, giving reasons for their responses as appropriate. Afterwards, ask:
● Where might we see or hear about millions in everyday life?
Teaching tip
While it is not essential that the children know the groups that follow millions, many of them might have encountered billions and trillions in the media. Others might be interested in the pattern of prefixes (billions, trillions, quadrillions, quintillions, etc.).
P Pupil’s Book page 10: Millions
Optional consolidation and extension possibilities
Maths Journal Use the Lesson 3 prompt from the Unit 1 Maths Journal Prompts PCM.
Display The children could contribute samples of their own work from this lesson and label them.
Games Bank Play ‘4 Spins to 1,000,000’ or ‘Spin and Place’.
Story Read How Much is a Million? by David M. Schwartz. A reading of the story is available at: edco.ie/snvg
Maths language
Integration History and Geography: Explore statistics with large numbers (e.g. casualties in battles and wars, population sizes, statistics about space and the planets).
STEM Maximise on opportunities to incorporate and explore numbers up to and in the millions, and decimal numbers to 4 places and beyond. For example, use technology to explore number sequences (e.g. Fibonacci numbers), or build scale models of large objects, such as bridges or buildings, and calculate/express the actual dimensions.
Integration Geography: Walk to a location that is a distance of 1km (i.e. 1 milllion mm) from the school, or use a GPS map to pinpoint a location that distance away on a map.
Estimation Station Estimate how many grains of rice there are in a 1kg bag. Ask the children: ‘How can we arrive at a good estimate without counting all of the grains?’ (Find out how many grains of rice there are in a tablespoon or scoop and then how many tablespoons/scoops can be filled from the bag; find out how many grains equal 1g/10g and multiply that number by 1000/100.) Next, using the first estimate, estimate how many 1kg bags of rice are needed to have more than 1 million grains.
Review and Reflect Use the prompt questions in the Review and Reflect Poster.
Day 6, Lesson 4
Estimating and Rounding
Numbers
Focus of learning (with Elements)
● Uses their skills of rounding and estimating (R)
Learning experiences
Digital activity: Which One Doesn’t Belong? – Estimating and Rounding
Numbers MAM Routines: Reason & Respond, with Think-Pair-Share
Video: Rounding Numbers
MAM Routines: Reason & Respond, with Write-Hide-Show
Concrete activity: Rounding Numbers MAM Routine: Write-Hide-Show
Pupil’s Book page 11: Estimating and Rounding Numbers
Maths language
Equipment
● There is no equipment needed for this lesson.
● estimate, roughly (approximately), closer to, between, round to one/two decimal place(s)
Warm-up
D Digital activity: Which One Doesn’t Belong?
– Estimating and Rounding Numbers
MAM Routines: Reason & Respond, with Think-Pair-Share
Play the slideshow and, using Think-Pair-Share, ask the children to propose reasons for why each does not belong. Encourage them to give reasons for their responses.
For possible reasons why each image doesn’t belong, go to the Information panel of this digital resource.
Main event
D Video: Rounding Numbers MAM Routines:
Reason & Respond, with Write-Hide-Show
Play the video and, using Write-HideShow, ask the children to respond to the questions on their MWBs, giving reasons for their responses as appropriate.
Afterwards, ask the children to round various whole and decimal numbers to a given place and to explain or demonstrate their strategy.
Allow time to discuss, display and compare the efficiency and accuracy of the strategies used.
Teaching tip
Ensure that the children realise that if a number is exactly half-way between both options, by convention, we round to the greater number
C Concrete activity: Rounding Numbers
MAM Routine: Write-Hide-Show
Write a 7-digit number (e.g. 2,934,517) on the board, and using Write-Hide-Show, ask/say:
● Round this number to the nearest million. How did you do it? What strategies did you use?
● Round this number to the nearest hundred thousand (or ten thousand, thousands, and so on). How did you do it? What strategies did you use?
Allow time for the children to justify their answer and/or explain or demonstrate their strategy. Discuss and compare the efficiency of the strategies used.
Repeat as required with other 7-digit numbers and a selection of decimal numbers.
Let’s deepen
As appropriate, challenge the children to:
● round the numbers to their nearest half thousand or half million.
● identify the most significant (important) digit in each number and how they might round a number to its most significant digit.
P Pupil’s Book page 11: Estimating and Rounding Numbers
Optional consolidation and extension possibilities
Maths Journal Use the Lesson 4 prompt from the Unit 1 Maths Journal Prompts PCM.
Display The children could contribute samples of their own work from this lesson and label them.
Maths Eyes Ask the children to identify and round real-world examples of large number facts (e.g. the population of Ireland or a nearby town or city, the cost of various cars or local houses, the capacities of major venues and sports stadia).
Large Number Scavenger Hunt Give the children specific examples to search for (e.g. a video with over 10,000 views, a website with over 100,000 visitors, a celebrity with over 500,000 followers, a song that has been streamed more than 1 million times).
Games Bank Play ‘Round Out Them Millions’, ‘Round Out Them Ones’, ‘Win Big Rounding’ or ‘Less is Best Rounding’.
Review and Reflect Use the prompt questions in the Review and Reflect Poster.
Days 7 and 8, Lesson 5
Positive and Negative Numbers
Focus of learning (with Elements)
● Identifies positive and negative numbers in context (U&C)
Learning experiences
Digital activity: Which is the Greatest Value? MAM Routines: Concept Cartoon, with Think-Pair-Share
Digital activity: The Elevator MAM Routine: Three-Act Task
Pupil’s Book pages 12–13: Positive and Negative Numbers
(*While acknowledging that the terms ‘plus’ and ‘minus’ are commonly used, it is more mathematically correct to use ‘positive’ and ‘negative’.)
Teaching tip
At primary level, positive and negative numbers can often be referred to as ‘directed’ numbers. However, it is more mathematically accurate to refer to them as integers, which is also the terminology that is used at post-primary level. Integers are the set of numbers that include all positive whole numbers (e.g. 1, 2, 3…), all negative whole numbers (e.g. –1, –2, –3…), and zero.
If you believe it will not overwhelm the children, introducing the term ‘integers’ now will be more beneficial for their long-term learning and ease the transition to post-primary maths. Maths and Me deliberately avoids the use of ‘directed’ numbers, as this will ultimately be discarded in favour of integers, and the use of interchangeable terminology may lead to confusion.
Warm-up
D Digital activity: Which is the Greatest Value?
MAM Routines: Concept Cartoon, with Think-Pair-Share
Display the Concept Cartoon, in which the characters are looking at the temperature in three cities and discussing which value they think is the greatest. Click to hear each character’s thoughts. Then, using Think-Pair-Share, ask:
● What do you think?
● (Point to a specific character.) Do you agree with their idea? Explain why.
● Do you think something different? What do you think?
● Why do you think this?
If appropriate, record the children’s responses to these questions on the board. Allow the children the opportunity to respond to (agree/disagree with or query) others’ responses, but do not confirm or reject any of the ideas.
● How can we find out who is correct?
Encourage the children to present their suggested approaches and/or solutions.
Main event
D Digital activity: The Elevator MAM Routine: Three-Act Task
This is a Three-Act Task to work out the final floor that an elevator stopped at.
Act 1: Notice & Wonder
Play the animation, which shows Jay using an elevator in a tall building.
Using Think-Pair-Share, click to play or ask:
● What do you notice?
● What do you wonder?
Record the children’s responses to both questions on the board. Allow the children the opportunity to respond to (agree/disagree with or query) others’ responses, but do not confirm or reject any of the ideas.
● (Reveal the focus question.) What was the final floor that Jay was at?
Act 2: Productive Struggle
Look at the image. Using Think-Pair-Share and Write-Hide-Show, click to play or ask:
● Write an estimate that is too high on your MWB.
● Write an estimate that is too low.
● Write a reasonable estimate.
The children work in pairs or small groups to answer the focus question. If necessary, prompt them by asking:
● Do you have enough information? What else do you need to know?
Once the children explain that they need to know more about the direction and number of floors travelled, click to flip the image over and play the next part of the animation. Click to play or ask:
● What information do you have now?
● To get an answer, what needs to be done?
● What strategies can you use?
Using Build it; Sketch it; Write it, the children choose their preferred way to mathematically model their strategies/solution(s).
Act 3: The Big Reveal
The children share and discuss their strategies and solutions. Click to play or ask:
● What answer did you get?
● What strategies did you use to get the answer?
● What do you think was the most efficient strategy?
Click to flip the card and play the final part of the animation to reveal the answer (the final floor Jay was at was -2). Click to play or ask:
● Is this the answer that you expected? Why or why not?
● What ‘I wonder’ questions did you answer?
● Do you have any new ‘I wonder’ questions?
Teaching tip
Maths Journals: The children could record, using images and/or words, what they built, sketched or wrote above
Let’s deepen
Challenge the children to create their own problems for others to solve (e.g. If Jay gets back on at -2, and he travels up 4 floors, what floor will he be on then?).
P Pupil’s Book pages 12–13: Positive and Negative Numbers
Optional consolidation and extension possibilities
Maths Journal Use the Lesson 5 prompt from the Unit 1 Maths Journal Prompts PCM. The children could also create their own personal fractions, decimals and percentages reference grid for the new equivalent forms they identified in this lesson in their Maths Journals.
Display The children could contribute samples of their own work from this lesson and label them.
Integration History: Create timelines of historical events using negative numbers to represent years BC.
STEM Maximise on opportunities to incorporate and explore the concept of positive and negative numbers. For example, investigate the effects of temperature changes on materials, or design containers that keep liquid at the same temperature for longer.
Review and Reflect Use the prompt questions in the Review and Reflect Poster.
Day 9, Lesson 6
Positive and Negative Numbers on the Number Line
Focus of learning (with Elements)
● Recognises negative numbers and extends regular patterns that include negative numbers (R)
Digital activity: Same But Different – Positive and Negative Numbers
MAM Routines: Reason & Respond, with Think-Pair-Share
Learning experiences ● There is no equipment needed for this lesson.
Concrete activity: Patterns in Positive and Negative Numbers
MAM Routines: Reason & Respond, with Write-Hide-Show
Pupil’s Book page 14: Positive and Negative Numbers on the Number Line
● pattern, symmetry
Warm-up
D Digital activity: Same But Different – Positive and Negative Numbers MAM Routines: Reason & Respond, with Think-Pair-Share
Play the slideshow and, using Think-Pair-Share, ask the children to propose reasons for why the images are the same and why they are different.
Main event
C Concrete activity: Patterns in Positive and Negative Numbers MAM Routines: Reason & Respond, with Write-Hide-Show
Using the same resource as in the Warm-up, and with slide 6 on display (showing the horizontal number line), ask:
● What patterns do you notice in the numbers?
● What do you notice about one and negative one, two and negative two, and so on? (In each pair, the numbers are the same distance from zero.)
● Is there a type of symmetrical pattern visible? If yes, where would the line of symmetry be? (at zero)
● What do you notice about the scale intervals used on each slide?
● Is zero always given? If zero is not always given, how might you identify its position?
Ask the children to use their MWBs to complete various number lines representing negative numbers (e.g. with zero in the middle and going from zero in intervals of 1, 2, 5, 10, 4).
Let’s strengthen
The children may benefit from turning their MWBs to create vertical number lines first, before rotating them back to the typical horizontal position.
P Pupil’s Book page 14: Positive and Negative Numbers on the Number Line
Optional consolidation and extension possibilities
Maths Journal Use the Lesson 6 prompt from the Unit 1 Maths Journal Prompts PCM. Games Bank Play ‘Tug o’ War!’. Online Games Play these games:
● ‘Placing Numbers on a Number Line’ (negative and positive numbers) at edco.ie/uqcf
● ‘Coconut Ordering’ (ordering positive and negative numbers) at edco.ie/7mtf
Display The children could contribute samples of their own work from this lesson and label them.
Digital Online Tools Use this tool to explore and locate positive and negative numbers on a number line using various intervals: edco.ie/uup8
Review and Reflect Use the prompt questions in the Review and Reflect Poster.
Day 10, Lesson 7
Review and Reflect
Focus of learning (with Elements)
● Reviews and reflects on learning (U&C)
Warm-up
Carry out a warm-up activity of your choice from one of the lessons in this unit.
Main event
Choose from this menu of activity ideas, or choose your own way to best structure this last lesson to suit your needs and the needs of your class.
Let’s talk!
Classroom poster: Review and Reflect
Use Think-Pair-Share alongside the prompt questions to review the unit. Individual children could present examples of their own drawings/work/ constructions to the class, and talk about what they have learned.
Maths language
Ask the children to explain the following terms (perhaps using examples or drawings on their MWBs): ones, tens, hundreds, thousands, millions, place value, base ten system, digit, comma, unnecessary/necessary zero, placeholder, compare, order, greater than (>), less than (<), fraction(s), decimal(s), point, whole, parts, divide, equal, tenth(s), hundredth(s), thousandth(s), standard form, expanded form, estimate, roughly (approximately), closer to, between, round to one/ two decimal place(s), negative, positive, above/ below zero, plus, minus, pattern, symmetry.
Use the Unit 1 Maths Language Cards to revise the key terms. For example: if the image and text are cut apart, can the children match them?
Progress Assessment Booklet
Complete questions xx–xx on pages xx–xx. Alternatively, these can be left to do as part of a bigger review during the next review week.
Let’s strengthen
Identify children who might benefit from extra practice with some of the key concepts or skills in this unit. Consult the Unit 1 Let’s Strengthen Suggestions for Teachers and/or use the Unit 1 Let’s Strengthen PCM.
Let’s play!
Play any of the games for Unit 1 from the Games Bank.
Play or use some of the online digital resources referenced in the unit (see the Optional Consolidation and Extension Possibilities throughout).
Maths strategies and models
Ask the children to give examples of the strategies they used in this unit (e.g. reading large and decimal numbers, estimating, rounding). Ask the children to give examples of the models they used in this unit (e.g. the ways that they can build, sketch and/ or write numbers). Which strategies and models did they prefer and why? What needs to be considered when choosing the ‘best’ strategy and model for each situation?
Maths eyes
Decimal Number Scavenger Hunt: Give the children specific examples to search for (e.g. a decimal number with one/two/three decimal places).
