100% coverage of New Zealand Mathematics and Statistics Curriculum for Phases 1-3
Proven results in New Zealand schools for over a decade Clear, step-by-step lessons for consistent, explicit teaching
Structured problem solving and reasoning for deep understanding
1. Add.
2. Subtract.
a) 742 –610
3. Round 3,527 to the
a) nearest ten.
b) nearest hundred.
c) nearest thousand.
4. Draw a bar model for each word problem.
a) Tina has 254 paper stars. Sophia gives her 58 more. How many paper stars does Tina have now?
b) 429 concert tickets were sold on Sunday. 64 more concert tickets were sold on Sunday than on Saturday. How many concert tickets were sold on Saturday?
333 student volunteers from Wellington took part in Ocean Alive's Aotearoa's Coastal Cleanup events in 2026. They collected 1,547 food wrappers and 820 more plastic drink bottles than food wrappers. How many food wrappers and plastic drink bottles did the volunteers collect altogether?
? 3,914
How can we solve this problem? Discuss in your group and fill in columns 1 and 2.
1. What I already know that will help me solve the problem
Add two 3-digit numbers. Solve 2-step word problems involving addition of 3-digit numbers.
2. What I need to find out and learn 3. What I have learnt 64 429
Add two 4-digit numbers. Solve 2-step word problems involving addition of 4-digit numbers. Answer varies.
You will learn to...
• add to 4-digit numbers without and with regrouping
• estimate sums
• solve 1-step word problems involving addition
Find the sum of 1,452 and 2,437.
1,452 2,437 3,889
Add from right to left.
1,452 + 2,437 =
The sum of 1,452 and 2,437 is .
Let's Do Let's Do
1. Find the sum of 3,475 and 2,521.
2,521
3,475 + 2,521 = The
2. Add.
1. Add.
2. Add.
Let's Learn Let's Learn
Find the sum of 1,634 and 2,085.
3 tens + 8 tens = 11 tens Regroup the tens. 11 tens = 1 hundred 1 ten 10 tens can be renamed as 1 hundred. 11 tens can be renamed as 1 hundred and 1 ten.
1. Find the sum of 4,653 and 1,524.
4,653 + 1,524 = The sum of 4,653 and 1,524 is . 4,653 1,524
2. Add.
1. Add.
2. Add.
Let's Learn Let's Learn
Find the sum of 2,561 and 1,972. 2,561 + 1,972
Let's Do Let's Do
1. Find the sum of 3,578 and 2,641.
3,578 + 2,641 = The sum of 3,578 and 2,641 is . 3,578 2,641
2. Add.
1. Add.
2. Add.
Find the sum of 2,793 and 3,408.
Let's Do Let's Do
1. Find the sum of 5,876 and 1,685.
5,876 1,685
5,876 + 1,685 = The
2. Add.
2. Add.
Find the sum of 3,392 and 5,741.
Estimated sum:
3,392 + 5,741 ≈ 3,000 + 6,000 = 9,000
Actual sum:
3,392 + 5,741 = 9,133
9,133 is about 9,000. The answer is reasonable.
Let's Do Let's Do
To estimate the sum, round each number to the nearest thousand, then add.
1. Estimate and then find the actual sum. Use your estimates to check if your answers are reasonable.
Estimates vary. Sample:
a) 6,493 + 3,110 ≈ + = 6,493 + 3,110 = Is your answer reasonable?
b) 2,649 + 5,317 ≈ + = 2,649 + 5,317 = Is your answer reasonable?
1. Estimate and then find the actual sum. Use your estimates to check if your answers are reasonable.
Estimates vary. Sample:
a) 276 + 2,390 b) 6,281 + 3,183 c) $6,905 + $2,198 d) $3,997 + $2,096
276 + 2,390 ≈ 300 + 2,000 = 2,300
276 + 2,390 = 2,666
Let's Practise Let's Practise P B Chapter 3: Exercise 1.5, page 30 9,603 6,000 9,000 Yes 7,966 3,000 8,000 Yes 5,000 3,000
$6,905 + $2,198 ≈ $7,000 + $2,000 = $9,000
$6,905 + $2,198 = $9,103
$3,997 + $2,096 ≈ $4,000 + $2,000 = $6,000
$3,997 + $2,096 = $6,093 6,281 + 3,183 ≈ 6,000 + 3,000 = 9,000 6,281 + 3,183 = 9,464
Let's Learn Let's Learn
1,951 people attended a drift car racing event at the speedway on Saturday. There were 1,207 more adults than children who attended the event on Saturday. 836 more people attended it on Sunday than on Saturday. How many people attended the drift car racing event on Sunday?
1 Plan what to do.
2
3
Work out the Answer.
4
Check if your answer is reasonable.
2,787 is about 2,800. My answer is reasonable. Understand the problem.
How many people attended the event on Saturday?
How many more people attended the event on Sunday than on Saturday? Which piece of information is not necessary? What do I have to find?
I can draw a bar model to compare the number of people who attended the event on each day.
+ Plus Solve the problem in another way.
More people attended the drift car racing event on Sunday than on Saturday. So, add 1,951 and 836 to solve the problem. Write each number in expanded form before adding. 1,000 + 1,700 + 80 + 7 = 1,000 + 1,000 + 700 + 80 + 7 = 2,787
2,787 people attended the drift car racing event on Sunday.
Compare the methods in steps 3 and 5. Which method do you prefer? Why?
Let's Do Let's Do 1. Understand 2. Plan 3. Answer 4. Check 5. Plus
Solve the word problems. Use or draw bar models to help you. Show your work clearly. Next, try solving each problem in a different way. Which method do you prefer? Why?
1. Understand 2. Plan 3. Answer 4. Check 5. Plus
1. Mrs Brown's family made 3,754 chocolate chip biscuits and 2,615 oat biscuits for a bake sale. They sold all the biscuits. How many biscuits did they bake altogether? 3,754 2,615 ?
2. A bakery sold 4,059 loaves of bread last month. It sold 1,879 more loaves of bread this month than last month. It baked 5,802 loaves of bread last month. How many loaves of bread were sold this month?
Tāpiri 6,369 5,938
More loaves of bread were sold this month. I should add.
Solve the word problems. Show your work clearly.
1. A library has 837 fiction books and 4,192 non-fiction books. 247 of the books are audiobooks. How many books does the library have altogether?
2. Ben scored 5,936 points in a game. He scored 1,465 fewer points than Tim. Ben played the game for 15 minutes. What was Tim's score?
3. A recycling centre collects 4,209 used plastic bottles each day. It collects 1,584 more tin cans than plastic bottles. How many tin cans does the centre collect each day?
4. A laptop costs $2,106. A television costs $1,164 more than the laptop. A camera costs $1,322 more than the laptop. How much does the camera cost?
5. A stationery store has 1,965 pencils and 3,027 pens. It stocks 4,778 pencils. How many pencils does the stationery store have now?
I have learnt to... add to 4-digit numbers without and with regrouping estimate sums solve 1-step word problems involving addition
>> Look at EXPLORE on page 30 again. Can you solve the problem now? What else do you need to know? 5,029 7,401 5,793 $3,428 6,743
You will learn to...
• subtract from 4-digit numbers without and with regrouping
• estimate differences
• solve 1-step word problems involving subtraction
Let's Learn Let's Learn
Find the difference between 3,765 and 1,421.
Subtract the ones. 1
Subtract the tens. 2
Subtract from right to left.
Subtract the hundreds. 3
Subtract the thousands. 4
3,765 – 1,421 =
The difference between 3,765 and 1,421 is .
Let's Do Let's Do
1. Find the difference between 4,273 and 2,252.
2. Subtract.
2. Subtract.
Find the difference between 4,817 and 1,396.
Subtract the ones.
8 hundreds and 1 ten can be renamed as 7 hundreds and 11 tens.
Regroup the hundreds and tens.
8 hundreds 1 ten = 7 hundreds 11 tens
Subtract the tens.
1 hundred = 10 tens
1. Find the difference between 5,483 and 2,328.
5,483 – 2,328 = The difference between 5,483 and 2,328 is .
2. Subtract.
Let's Practise Let's Practise
1. Subtract.
2. Subtract.
Find the difference between 3,560 and 1,824.
4,473 – 2,615 = The difference between 4,473 and 2,615 is . 1. Find the difference between 4,473 and 2,615. Let's Do Let's Do
2. Subtract.
Let's Practise Let's Practise
1. Subtract.
Subtract.
Let's Learn Let's Learn
1. Find the difference between 7,261 and 4,589.
7,261 – 4,589 = The difference between 7,261 and 4,589 is .
2. Subtract.
Let's Practise Let's Practise
1. Subtract.
2. Subtract.
Let's Learn Let's Learn
a) Find the difference between 5,000 and 1,519. 5,000 – 1,519 = 3,481 The difference between 5,000 and 1,519 is 3,481.
There are no hundreds, tens and ones to subtract 1,519 from.
b) Find the difference between 6,400 and 3,972.
Subtract the ones.
6,400 – 3,972 = The difference between 6,400 and 3,972 is .
6 thousands 3 hundreds = 5 thousands 13 hundreds
Subtract the hundreds. Subtract the thousands.
Let's Do Let's Do
1. Find the difference between 8,000 and 2,375.
8,000 – 2,375 = The difference between 8,000 and 2,375 is . 2. Subtract.
Let's Practise Let's Practise 1. Subtract.
2. Subtract.
Find the difference between 6,346 and 3,482.
Estimated difference:
6,346 – 3,482 ≈ 6,000 – 3,000 = 3,000
Actual difference:
6,346 – 3,482 = 2,864
2,864 is about 3,000. The answer is reasonable.
To estimate the difference, round each number to the nearest thousand, then subtract.
1. Estimate and then find the actual difference. Use your estimates to check if your answers are reasonable.
a) 4,548 – 1,839 ≈ – = 4,548 – 1,839 = Is your answer reasonable?
b) 9,273 – 2,472 ≈ – = 9,273 – 2,472 = Is your answer reasonable?
2,709 5,000 3,000 Yes 6,801 9,000 7,000 Yes 2,000 2,000
Let's Practise Let's Practise
1. Estimate and then find the actual difference. Use your estimates to check if your answers are reasonable. a) 6,950 – 235 b) 8,562 – 4,437
Estimates vary. Sample:
Estimates vary. Sample: 6,950 – 235 ≈ 7,000 – 200 = 6,800 6,950 – 235 = 6,715
$5,447 – $2,669
$5,447 – $2,669 ≈ $5,000 – $3,000 = $2,000 $5,447 – $2,669 = $2,778 $6,374 – $4,628 ≈ $6,000 – $5,000 = $1,000 $6,374 – $4,628 = $1,746 8,562 – 4,437 ≈ 9,000 – 4,000 = 5,000 8,562 – 4,437 = 4,125
$6,374 – $4,628
A factory makes 5,732 items of clothing each day. 2,495 of them are hoodies and the rest are T-shirts. How many T-shirts does the factory make each day? Let's Learn Let's Learn Understand the problem.
1 Plan what to do.
3
2 Work out the Answer.
I can draw a bar model to show the number of items of clothing the factory makes each day.
How many items of clothing are made each day? How many hoodies are made each day? What do I have to find? Check if your answer is correct.
4 My answer is correct. 2,495 + 3,237 = 5,732, which is the total number of items of clothing the factory makes each day. My answer is correct.
+ Plus Solve the problem in another way.
The factory makes hoodies and T-shirts. So, subtract 2,495 from 5,732 to solve the problem. Write each number in expanded form before subtracting.
3,000 + 200 + 30 + 7 = 3,237 The factory makes 3,237 T-shirts each day.
Compare the methods in steps 3 and 5. Which method do you prefer? Why?
1. Understand 2. Plan 3. Answer 4. Check 5. Plus
Solve the word problems. Use or draw bar models to help you. Show your work clearly. Next, try solving each problem in a different way. Which method do you prefer? Why?
1. Understand 2. Plan 3. Answer 4. Check 5. Plus
1. A potato farmer dug 2,608 potatoes from his field. 254 of these potatoes were rotten. How many potatoes were not rotten?
2. A South Island sheep and beef farm has 5,893 cows and 3,687 sheep. It sold 1,904 cows. How many cows are left?
Tāpiri 2,354 3,989
The farm sold cows. There are fewer cows now. I should subtract.
Solve the word problems. Show your work clearly.
1. Village X has 8,431 people. Village Y has 2,638 fewer people than village X. How many people are there in village Y?
2. Phoebe earned $5,003 in a month. Tom earned $3,485 in the same month. How much more money did Phoebe earn than Tom?
3. At a school fair, 7,500 loot bags are being given away on a first-come-first-serve basis. About 9,000 people attended the fair. 4,618 loot bags have been given out so far. How many loot bags are left?
4. Factory A and factory B produce 4,793 cans each day. Factory A produces 2,305 cans each day. How many cans does factory B produce each day?
5. 8,000 people visited a carnival on a Sunday. 4,507 children and 3,493 adults visited the carnival. How many fewer adults than children visited the carnival?
6. An orchard has 2,409 apple trees. The orchard has 428 more apple trees than kiwifruit trees. How many kiwifruit trees does the orchard have?
P B Chapter 3: Exercise 2.7, pages 39–40 I have learnt to... subtract from 4-digit numbers without and with regrouping estimate differences solve 1-step word problems involving subtraction 1,981 5,793 $1,518 2,882 2,488 1,014
You will learn to...
• determine if a number sentence involving addition and subtraction is true or false
• complete open number sentences involving addition and subtraction
3.1 True or false number sentences involving addition and subtraction
a) Is 3,617 + 182 = 1,891 + 1,908 true or false?
3,617 + 182 = 3,799
1,891 + 1,908 = 3,799
So, 3,617 + 182 = 1,891 + 1,908 is true.
b) Is 2,105 – 76 = 2,303 – 294 true or false?
2,105 – 76 = 2,029
2,303 – 294 = 2,009
So, 2,105 – 76 = 2,303 – 294 is false.
c) Is 4,509 – 1,821 = 1,096 + 1,592 true or false?
Start with the left side of the equal sign.
Subtract 1,821 from 4,509.
4,509 – 1,821 = 1,096 + 1,592 =
A number sentence is true when both sides of the equal sign give the same answer. 2,688 2,688
Then, work on the right side of the equal sign. Add 1,096 and 1,592.
So, 4,509 – 1,821 = 1,096 + 1,592 is .
Do Let's Do
1. Are the number sentences true or false? Write the missing numbers. Then, write true or false in each blank.
a) 1,374 – 78 = 1,476 – 191 b) 4,265 – 112 = 1,276 + 2,877
4,153 4,153
1,374 – 78 = 4,265 – 112 = 1,476 – 191 = 1,276 + 2,877 = 1,374 – 78 = 1,476 – 191 is . 4,265 – 112 = 1,276 + 2,877 is .
1. Are the number sentences true or false? Show your work clearly. Then, write true or false in each blank. Let's Practise a) 1,920 + 92 = 2,012 1,920 + 92 = 2,012 is .
1,920 + 92 = 2,012 4,726 – 3,209 = 1,517
4,726 – 3,209 = 1,517 4,726 – 3,209 = 1,517 is . c) 1,820 + 2,900 = 2,183 + 2,517
5,019 – 2,325 = 4,600 – 1,806 5,019 – 2,325 = 4,600 – 1,806 is . e) 4,015 + 1,086 = 9,000 – 3,899
1,820 + 2,900 = 2,183 + 2,517 is
1,820 + 2,900 = 4,720 2,183 + 2,517 = 4,700 5,019 – 2,325 = 2,694 4,600 – 1,806 = 2,794 4,015 + 1,086 = 5,101 9,000 – 3,899 = 5,101 8,500 – 2,817 = 5,683 3,726 + 1,817 = 5,543
4,015 + 1,086 = 9,000 – 3,899 is . f) 8,500 – 2,817 = 3,726 + 1,817 8,500 – 2,817 = 3,726 + 1,817 is .
Let's Learn Let's Learn
a)
5,442 + 179 = ☆ + 2,386
Find the value of ☆.
5,442 + 179 = ☆ + 2,386 5,612 = ☆ + 2,386 ☆ = 5,612 – 2,386 =
So, 5,442 + 179 = + 2,386.
The value of ☆ is .
b) – 1,821 = 1,271 + 3,900
Find the value of . – 1,821 = 1,271 + 3,900 – 1,821 = 5,171 = 5,171 + 1,821 = So, – 1,821 = 1,271 + 3,900. The value of is .
5,1711,821 3,235 3,235 3,235 6,992 6,992 6,992
1. Complete the number sentences to find the missing values. a) 2,117 – 25 = 3,600 – ✧ = 3,600 – ✧ ✧ = 3,600 –= Let's Do Let's Do
Let's Practise Let's Practise
1. Find the missing values. Show your work clearly.
4,190 = 1,582 + Δ
1,800 + 1,200 = 2,932 + ✿
= 7,250 –
= 4,190 – 1,582 = 2,608 ☆ = 7,250 – 3,287 = 3,963 6,561 = 9,827 – ✧
– 2,367 = 9,827 –
= 4,000 –= I have learnt to... determine if a number sentence involving addition and subtraction is true or false complete open number sentences involving addition and subtraction
= 9,827 – 6,561 = 3,266 3,266 3,000 = 2,932 + ✿ ✿ = 3,000 – 2,932 = 68
3,274 + 2,940 = ◇ – 3,518
2,608 3,963 6,214 = ◇ – 3,518 ◇ = 6,214 + 3,518 = 9,732 5,619 = ◇ + 2,934 ◇ = 5,619 – 2,934 = 2,685 9,732 2,685
8,000 – 2,381 = ◇ + 2,934
You will learn to...
• solve 2-step word problems involving addition and subtraction
• solve non-routine problems involving addition and subtraction
Let's Learn Let's Learn Understand the problem.
Mr Peters furnished his home in February and March. He spent $4,863 in February. He spent $1,965 less in March. How much did he spend in February and March altogether?
1 Plan what to do. 2 Work out the Answer. 3
Mārama
I can draw a bar model to compare the amounts of money Mr Peters spent in February and in March.
$4,863 – $1,965 = $2,898 He spent $2,898 in March.
$4,863 + $2,898 = $7,761 He spent $7,761 in February and March altogether. How much did he spend in February? How much less did he spend in March? What do I have to find?
Compare the methods in steps 3 and 5. Which method do you prefer? Why? Check if your answer is correct. 4 + Plus Solve the problem in another way. 5
$2,898 + $1,965 = $4,863
Mr Peters spent $4,863 in February.
$7,761 – $2,898 = $4,863
Mr Peters spent $4,863 in February.
My answer is correct. $4,863
The amount of money Mr Peters spent in March is $1,965 less than $4,863. We can first add $4,863 and $4,863. Then, we subtract $1,965.
$4,863 + $4,863 = $9,726 $9,726 – $1,965 = $7,761 He spent $7,761 in February and March altogether.
Solve the word problem. Draw a bar model to help you. Show your work clearly. Next, try solving the problem in a different way. Which method do you prefer? Why?
1. A bakery sold 1,695 pies last week. It sold 210 more pies this week than last week. How many pies were sold in both weeks?
More pies were sold this week than last week. I should add. Tirohia
Solve the word problems. Show your work clearly.
1. Printer A can print 1,374 pages in one hour. Printer B can print 128 more pages than printer A in one hour. How many pages can both printers print altogether in one hour?
2. The total mass of a horse and a giraffe is 1,386 kilograms. The horse has a mass of 585 kilograms. A pony is 480 kilograms lighter than the horse. Find the difference between the mass of the horse and the mass of the giraffe.
3. 7,402 adults took part in a run. 5,963 of them were men. The rest were women. How many more men than women took part in the run?
4. Leah collected 8,000 ring tabs for her art projects. She used 4,915 ring tabs for her first project and 2,586 ring tabs for her second project. How many ring tabs did she have left?
499
5. A farm had 1,296 cows, 1,113 sheep and 260 chickens at first. Then, the farm sold 264 sheep. How many cows and sheep were left?
kg 2,145
YOUR OWN
Use the given words and amounts to write a 2-step word problem. How did you come up with the word problem?
Next, solve the word problem. Show your work clearly. What did you learn?
David has $3,267. Maia has $1,089 more than David. How much money do they have altogether?
$3,267 + $1,089 = $4,356 $4,356 + $3,267 = $7,623
They have $7,623 altogether.
Let's Learn Let's Learn Understand the problem.
Carpark A has 4,687 cars parked in it. Carpark B has 4,667 cars parked in it. How many cars should move from carpark A to carpark B so that both carparks have the same number of cars?
1 Plan what to do.
How many cars are there in carpark A? How many cars are there in carpark B? What do I have to find?
2
3
Whakaaro
I can draw a bar model to show the number of cars in each carpark.
Work out the Answer
Whakaatu Mārama
carpark A
carpark B
4,687 – 4,667 = 20
There are 20 more cars in carpark A than in carpark B.
The 20 cars have to be distributed equally between the two carparks.
1 + 1 = 2
10 + 10 = 20 10 cars should move from carpark A to carpark B. 4,667 4,687 ?
I can use double facts to help me.
5
4 + Plus Solve the problem in another way.
Check if your answer is correct.
Tirohia
4,687 – 10 = 4,677
Carpark A will have 4,677 cars left. 4,667 + 10 = 4,677
Use guess and check to solve the problem. First, guess how many cars should move from carpark A to carpark B. Then, work out the number of cars in carpark A and carpark B.
Carpark B will also have 4,677 cars. My answer is correct. GuessCarpark ACarpark BA = B?
10 cars should move from carpark A to carpark B. Compare the methods in steps 3 and 5. Which method do you prefer? Why?
Olive wants to subtract a 4-digit number from a greater 4-digit number. The digit in the hundreds place of the greater number is double the digit in the hundreds place of the number that is less. Find the two numbers.
Strategy: Work backwards and guess and check
To find the greater number, we can work backwards by adding the number that is less to the difference.
(1) Look at the ones.
6 + ? = 0 or 6 + ? = 10
Since the sum cannot be less than 6, the correct sum should be 10.
6 + ? = 10
6 + 4 = 10
So, the digit in the ones place is 4.
So,
We regroup 10 ones to 1 ten.
(2) Look at the tens.
Add the digits:
1 + 6 + 3 = 10
Regroup 10 tens to 1 hundred.
So, the digit in the tens place is 0.
So, place
Guess and check:
(3) Look at the hundreds.
The digit in the hundreds place for the number that is less is ‘3’. The digit in the hundreds place for the greater number is ‘6’.
(4) Look at the thousands.
3 + 5 = 8
+53 34 8 6 0 0 Digit in the number that is less Digit in the greater number Check 1 2 1 + 2 + 1 = 4 ✗ 2 4 1 + 2 + 2 = 5 ✗ 3 6 1 + 2 + 3 = 6 ✓ (6 is double 3.) 4 8 1 + 2 + 4 = 7 ✗ 5 10 ‘10’ is not possible as it is 2-digit number.
The two numbers are 8,600 and 5,334.
I have learnt to... solve 2-step word problems involving addition and subtraction solve non-routine problems involving addition and subtraction
>> Look at EXPLORE on page 30 again. Fill in column 3. Can you solve the problem now?