Multiplying Larger Numbers: a week of ready-to-teach maths

Five days of lessons for Year 5 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus digit cards with two product mats, eight camp problem cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the digit cards and the camp cards once; the digit cards come back on three days.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: a big multiplication is a few small ones. Split a number by place value, multiply each part and add the parts: 236 × 4 = 800 + 120 + 24 = 944. Two two-digit numbers make four parts, and a grid keeps them in order. Then look at the numbers before choosing how to work, and check every answer against an estimate: 48 × 21 is about 50 × 20 = 1000.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

Calculators

The curriculum asks children to use digital tools where they help. On Days 3 and 4 they use a calculator for the biggest products, always after an estimate, and the estimate catches a slip of the finger. One calculator per pair is enough. On the other days the work is mental or on paper.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Days 1 and 2 split by place value, first one number and then both; Day 3 chooses the quickest way, a calculator included; Day 4 checks answers against estimates; and Day 5 puts it all together in camp problems. It builds on Year 4’s efficient strategies and estimation (AC9M4N06, AC9M4N07), and it leads to division later this year (AC9M5N07) and to Year 6, where children model practical problems with natural numbers, fractions, decimals and percentages (AC9M6N09).

Materials for the week (one trip)

• From the classroom: scissors, envelopes for the cards, rulers, mini whiteboards, this pack printed.
• For Days 3 and 4: one calculator per pair.
• Cut out once, use all week: the digit cards and product mats (Days 1, 2 and 5) and the eight camp cards (Day 5). No maths equipment to buy.

Words for the word wall

product, partition, place value, partial product, area model, estimate, round, reasonable, efficient, strategy, calculator

Dear families

This week in maths, Year 5 multiplies larger numbers. We split a number by place value and multiply each part: 236 × 4 = 200 × 4 + 30 × 4 + 6 × 4 = 800 + 120 + 24 = 944. Then we check the answer with an estimate: 48 × 21 is about 50 × 20, which is 1000.

Try this at home

• A box holds 24 muesli bars. How many bars are in 6 boxes? Split 24 into 20 and 4.
• How many days are in 52 weeks? Work out 52 × 7 by splitting 52 into 50 and 2.
• Before you use a phone calculator, guess the answer together. Is the calculator answer close to the guess?
• Ask your child why 23 × 14 is not 20 × 10 + 3 × 4.

My multiplications this week

Fill one row a day. Find something at home to multiply, estimate first, then work it out.

Printed from the free seegongsik Multiplying Larger Numbers teaching pack · seegongsik.com/au/y5/number/AC9M5N06/pack

Split by place value

Children multiply two-, three- and four-digit numbers by a one-digit number by splitting the bigger number by place value: 236 is 200, 30 and 6. Each part is multiplied, and the partial products are added. A split frame keeps every part in view.

We are learning to

• split a number into thousands, hundreds, tens and ones,
• multiply each part by a one-digit number, then add the partial products,
• use the biggest part to check that the total makes sense.

Success criteria

• I can work out 236 × 4 by splitting 236 into 200, 30 and 6.
• I can explain why 307 × 4 has only two parts to add.

You need

Digit cards and Mat 1 (cut-out sheet 1), one sheet per pair. Mini whiteboards. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by splitting 527 × 3 together.

Watch for these ideas

• Multiplying only one part, so 23 × 4 = 80 + 3 = 83. Every part is multiplied by 4.
• Losing the place value: 2 × 4 + 3 × 4 + 6 × 4 for 236 × 4. Say the parts as numbers: two hundred, thirty, six.
• Reading 307 as 30 and 7. The 3 is three hundreds; the zero says there are no tens.

Answers

• Part A: 47 × 3 = 40 × 3 + 7 × 3 = 120 + 21 = 141; 258 × 4 = 200 × 4 + 50 × 4 + 8 × 4 = 800 + 200 + 32 = 1032. Part B: 448, 1000, 1710, 1917, 1458, 9260.
• Part C: 1200 + 28 = 1228; 3000 + 45 = 3045; 3500 + 280 = 3780; two parts each, as a zero digit gives no part. Part D: biggest 752 × 9 = 6768 (975 × 2 is only 1950); smallest 579 × 2 = 1158.

Split by place value

A. Split the number, multiply each part, then add

B. Split and multiply

64 × 7 = ________125 × 8 = ________342 × 5 = ________213 × 9 = ________486 × 3 = ________2315 × 4 = ________

C. A zero in the number

307 × 4 = ________609 × 5 = ________540 × 7 = ________

How many parts did you add each time? Why? _________________________________________

D. Card game

Take the cards 2, 5, 7 and 9. Put them on Mat 1 as a three-digit number times a one-digit number. Find the biggest product you can, then the smallest.

Biggest: _____ × ___ = _______     Smallest: _____ × ___ = _______

Four parts on a grid

Children multiply two two-digit numbers on an area grid. Both numbers are split by place value, the parts go across the top and down the side, and each cell holds one partial product. Adding every cell gives the product: 23 × 14 = 200 + 30 + 80 + 12 = 322.

We are learning to

• split both numbers by place value and set them on a grid,
• find each cell’s partial product, then add all the cells,
• use a wider grid for a three-digit number times a two-digit number.

Success criteria

• I can work out 36 × 24 on a grid and show all four partial products.
• I can explain why 23 × 14 is not 20 × 10 + 3 × 4.

You need

Digit cards and Mat 2 (cut-out sheet 1), one sheet per pair. Rulers. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by labelling a grid for 52 × 17 together.

Watch for these ideas

• Multiplying tens by tens and ones by ones only, so 23 × 14 = 200 + 12. A grid has four cells; fill every one.
• Adding the labels instead of multiplying them: 20 and 10 make 30. Each cell is a multiplication, 20 × 10 = 200.
• Dropping zeros, so 30 × 20 = 60. Three tens times two tens is six hundreds: 600.

Answers

• Part A: 46 × 23 = 800 + 120 + 120 + 18 = 1058; 45 × 12 = 400 + 50 + 80 + 10 = 540. Part B: 27 × 16 = 200 + 70 + 120 + 42 = 432; 53 × 31 = 1500 + 90 + 50 + 3 = 1643; 68 × 25 = 1200 + 160 + 300 + 40 = 1700.
• Part C: 124 × 13 = 1000 + 200 + 40 + 300 + 60 + 12 = 1612; 215 × 22 = 4000 + 200 + 100 + 400 + 20 + 10 = 4730. Part D: biggest 83 × 75 = 6225 (87 × 53 is only 4611); smallest 58 × 37 = 2146. Either order counts.

Four parts on a grid

A. Fill in the grid, then add

B. Write the labels, fill in the grid, then add

C. A wider grid: a three-digit number times a two-digit number

D. Card game

Take the cards 3, 5, 7 and 8. Put them on Mat 2 as two two-digit numbers. Find the biggest product you can, then the smallest. Use a grid to check each one.

Biggest: ____ × ____ = _______     Smallest: ____ × ____ = _______

Look at the numbers first

Children choose a strategy to suit the numbers: 99 × 6 is quicker as 100 × 6 − 6, and 25 × 16 as 50 × 8. For a four-digit number times a two-digit number, a calculator is the right tool, after an estimate.

We are learning to

• look at the numbers before choosing a strategy,
• round and adjust, or double and halve, when the numbers invite it,
• decide when a calculator is the better tool, and estimate first.

Success criteria

• I can work out 99 × 6 as 100 × 6 − 6 and say why it works.
• I can choose a strategy for a product and give a reason.

You need

One calculator per pair. Mini whiteboards. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by modelling 25 × 12.

Watch for these ideas

• Adjusting by the wrong amount: 99 × 6 = 600 − 1. Each of the six 99s is 1 short, so take away 6.
• Doubling both numbers: 25 × 16 as 50 × 32. Double one, halve the other, and the product stays the same.
• Reaching for the calculator first, or trusting it without an estimate. Estimate, key in, then compare.

Answers

• Part A: 99 × 7 = 700 − 7 = 693; 49 × 6 = 300 − 6 = 294; 199 × 4 = 800 − 4 = 796; 101 × 8 = 800 + 8 = 808; 98 × 5 = 500 − 10 = 490. Part B: 25 × 16 = 50 × 8 = 400; 15 × 18 = 30 × 9 = 270; 35 × 4 = 70 × 2 = 140; 45 × 22 = 90 × 11 = 990; 125 × 8 = 250 × 4 = 1000.
• Part C (any strategy done correctly counts): 99 × 9 = 891, round and adjust; 25 × 24 = 600, double and halve; 342 × 3 = 1026, split; 213 × 4 = 852, split; 199 × 3 = 597, round and adjust; 35 × 16 = 560, double and halve. Part D: 4386 × 27 = 118 422 (about 4000 × 30 = 120 000); 2789 × 46 = 128 294 (about 3000 × 50 = 150 000); 3604 × 58 = 209 032 (about 4000 × 60 = 240 000).

Look at the numbers first

A. Round, multiply, then adjust

99 × 7 = ________ = ______49 × 6 = ________ = ______199 × 4 = ________ = ______101 × 8 = ________ = ______98 × 5 = ________ = ______

B. Double one number, halve the other

25 × 16 = ________ = ______15 × 18 = ________ = ______35 × 4 = ________ = ______45 × 22 = ________ = ______125 × 8 = ________ = ______

C. Choose a strategy, then work it out

D. Estimate, then use a calculator

Estimate, then check

Children estimate by rounding each number to its first digit, then judge answers against the estimate. About ten times too big or too small means a slipped digit; close to the estimate means reasonable, though not always right.

We are learning to

• round each number to its first digit to estimate a product,
• decide whether an answer is reasonable by comparing it with the estimate,
• find the slip when an answer, or a calculator screen, is far from the estimate.

Success criteria

• I can estimate 48 × 21 as 50 × 20 = 1000.
• I can explain why 920 cannot be 23 × 4.

You need

One calculator per pair. Mini whiteboards. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 27 × 31 worked out as 8370.

Watch for these ideas

• Rounding the one-digit number too: 312 × 7 as 300 × 10. A one-digit number stays as it is.
• Thinking an answer close to the estimate must be right. Close means reasonable; check the working too.
• Trusting the calculator screen. A slip of the finger is as easy as a slip of the pencil, so estimate first.

Answers

• Part A: 2000 (50 × 40), 1200 (60 × 20), 2100 (300 × 7), 3600 (90 × 40), 3000 (500 × 6), 900 (30 × 30). Part B: 246 yes, and right; 8360 no (about 800), right answer 836; 160 no (about 1800), right answer 1600; 820 yes, and right; 1289 yes (about 1800) but wrong, right answer 1829; 3222 no (about 350), right answer 322.
• Part C: Lily: about 40 000, so 4374 is far off; keyed 243 × 18, leaving out a digit; 2436 × 18 = 43 848. Ned: about 8000, so 389 is far off; pressed + instead of × (365 + 24 = 389); 365 × 24 = 8760. Part D: any product; the partner’s estimate should catch the slip.

Estimate, then check

A. Round each number to its first digit, then estimate

52 × 38 is about ____ × ____ = ______61 × 19 is about ____ × ____ = ______312 × 7 is about ____ × ____ = ______89 × 42 is about ____ × ____ = ______497 × 6 is about ____ × ____ = ______28 × 33 is about ____ × ____ = ______

B. Reasonable or not? Estimate, then work out the right answer

C. Calculator slips

D. Catch my slip

Write a product and a wrong answer with one slipped digit. Swap with a partner. Your partner estimates, circles the answer if it is not reasonable, and writes the right one.

My product: __________ = __________     My partner’s estimate: __________

Plan the camp

Children solve problems from a Year 5 camp. For each card they write the number sentence, estimate, choose a strategy, calculate and check, then answer in the words of the card with its unit.

We are learning to

• decide that a problem needs multiplication and write the number sentence,
• choose a strategy, calculate, and check the answer against an estimate,
• answer in the words of the problem, with the unit.

Success criteria

• I can solve a camp card and write the answer as a sentence with its unit.
• I can show my estimate next to my answer.

You need

The camp cards (cut-out sheet 2), one set per group of four. Digit cards and Mat 2 for early finishers. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first four cards; start Session B with Part B.

Watch for these ideas

• Adding the numbers in a story: 14 cabins and 8 children each as 22. Ask how many groups there are, and how many in each.
• An answer with no unit or dollar sign: 1344 for the lunches. The card asks for a cost, so the answer is $1344.
• Stopping after the first step of Part B. The bars ordered are not the bars left over.

Answers

• Camp cards (estimate in brackets): A 57 × 3 = 171 seats (180); B 14 × 8 = 112 children (80); C 112 × 12 = $1344 (1000); D 236 × 2 = 472 km (400); E 25 × 18 = $450 (600); F 48 × 23 = 1104 muesli bars (1000); G 1250 × 5 = 6250 litres (5000); H 112 × 19 = $2128 (2000).
• Part B: 23 × 48 = 1104 bars ordered, 112 × 9 = 1008 eaten, 1104 − 1008 = 96 bars left over. Part D: 45 × 12 = 540, with any story of 45 groups of 12. Card game: biggest 94 × 86 = 8084, smallest 69 × 48 = 3312.

Plan the camp

A. Camp planner: choose four cards

B. Two steps

The cook orders 23 boxes of 48 muesli bars. Over the camp, each of the 112 children eats 9 bars. How many bars are left over?

Bars ordered: __________    Bars eaten: __________    Bars left over: __________

C. Answer in a sentence

Choose one of your cards. Write the answer as a sentence that answers the card’s question.

Card ____: ____________________________________________________________

_____________________________________________________________________

D. Your turn

Write a camp problem that 45 × 12 answers. Then solve it, with an estimate.

_____________________________________________________________________

Estimate: __________    Answer: __________

Product mats and digit cards

One sheet per pair. Keep the two mats whole and cut out the two sets of digit cards, 1 to 9. Lay four cards on a mat to make a multiplication, work out the product, then move the cards to make the biggest product you can, and the smallest.

Teacher note: the cards fit the mat boxes. There is no zero card, so no number starts with zero. Each card game this week uses four cards from one set; the best arrangements are on the Day 1, Day 2 and Day 5 plans.

Camp cards

Year 5 is planning a camp. Cut out the eight cards (Day 5). For each card, write the number sentence, estimate, work out the answer and check it against the estimate.

Teacher note: the answers to all eight cards are on the Day 5 plan.

What we know: Multiplying Larger Numbers

Work on your own. Show your thinking if you can.

1. Split, then multiply:   46 × 7 = __________
2. Split, then multiply:   318 × 4 = __________
3. Fill in the grid for 34 × 26, then add.
   34 × 26 = __________
4. Round and adjust:   99 × 8 = __________
5. Double and halve:   25 × 28 = __________
6. Estimate by rounding each number:   61 × 49 is about __________
7. Mia says 52 × 31 = 16 120. Is that reasonable? Explain, and write the right answer.
8. A school buys 28 boxes of pencils. Each box holds 36 pencils. How many pencils is that?   __________

Answers and marking guide

Answers

1. 280 + 42 = 322
2. 1200 + 40 + 32 = 1272
3. 600 + 80 + 180 + 24 = 884
4. 800 − 8 = 792
5. 50 × 14 = 100 × 7 = 700
6. 60 × 50 = 3000
7. Not reasonable: about 50 × 30 = 1500, and 16 120 is ten times too big. 52 × 31 = 1612.
8. 28 × 36 = 600 + 240 + 120 + 48 = 1008 pencils.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by naming the parts they multiplied or the estimate they checked against.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: splitting by place value, the area grid, choosing a strategy, estimating to check, and solving problems.