Efficient Strategies: a week of ready-to-teach maths

Five days of lessons for Year 4 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out number cards and strategy-sort 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 two card sheets once; the cards are reused all week.
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 is choice. There is no single right way to work out 47 + 19; there is a quick way that fits the numbers. Children learn four mental strategies, then the most important skill of all: looking at the numbers before choosing.

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.

Where calculators fit

The descriptor asks for appropriate digital tools as well as mental strategies. A calculator is the efficient tool for 4826 + 3975, and a slow one for 7 × 9. On Day 5 children estimate first, then use a calculator, and check that the answer is close to the estimate.

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 give two strategies for adding and subtracting; Days 3 and 4 give two for multiplying and dividing; and Day 5 puts them side by side so children choose, with a calculator for the numbers that call for one. It builds on place value and the times tables, and leans on multiplying by 10 from the unit before.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• For Day 5: a few calculators, one per group (a tablet calculator is fine).
• Cut out once, use all week: the number cards and the strategy-sort cards in this pack.

Words for the word wall

strategy, efficient, split, tens, ones, round, adjust, take back, add back, parts, known fact, no remainder, estimate, calculator

Dear families

This week in maths, Year 4 learns quick ways to calculate in their heads: splitting numbers into tens and ones, rounding and adjusting, multiplying in parts, and dividing with a known fact. We also learn when a calculator is the better tool, and to estimate first.

Try this at home

• At the shops: $47 and $19 is about $47 and $20, then take back $1. So $66.
• Ask for 4 lots of 23 by thinking 4 lots of 20 and 4 lots of 3.
• Share 84 grapes between 4 people: 80 shared by 4 is 20 each, and 4 more is 1 each.
• Before using the calculator on your phone, guess the answer. Was the calculator close to your guess?

My quick ways this week

Fill one row a day. Write a sum or a product, and the quick way you used.

Printed from the free seegongsik Efficient Strategies teaching pack · seegongsik.com/au/y4/number/AC9M4N06/pack

Split into tens and ones

Children add two-digit numbers in their heads by splitting each number into tens and ones: 38 + 47 is 30 + 40 and 8 + 7, which is 70 + 15, or 85. They subtract by taking away the tens first, then the ones: 86 − 34 is 86 − 30 − 4.

We are learning to

• split two-digit numbers into tens and ones to add them mentally,
• put the tens total and the ones total back together, even when the ones make a new ten,
• subtract by taking away the tens of the second number, then its ones.

Success criteria

• I can add two two-digit numbers in my head by splitting them.
• I can explain my split in words.

You need

The number cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 86 − 34.

Watch for these ideas

• Adding the tens digits as ones: 3 + 4 = 7, then 7 + 15 = 22. Say the tens as tens: thirty and forty.
• Losing the new ten: 70 + 15 written as 715. Fifteen is one ten and five ones.
• Taking the smaller ones digit from the bigger: 72 − 45 done as 5 − 2 = 3 gives 33. Take away 40, then 5: 32 − 5 = 27.

Answers

• Part A: 34 + 25: 50 + 9 = 59; 47 + 38: 70 + 15 = 85; 59 + 26: 70 + 15 = 85; 73 + 18: 80 + 11 = 91.
• Part B: 86 − 34 = 56 − 4 = 52; 75 − 42 = 35 − 2 = 33; 93 − 51 = 43 − 1 = 42. Part C: any three card sums, split correctly.

Split into tens and ones

A. Add by splitting

B. Subtract the tens, then the ones

86 − 34= 86 − 30 − 4 = ______ − 4 = ______

75 − 42= 75 − 40 − 2 = ______ − 2 = ______

93 − 51= 93 − 50 − 1 = ______ − 1 = ______

C. Card sums with a partner

______ + ______ = ______    ______ + ______ = ______    ______ + ______ = ______

Under each one, write the split you used.

Round, then adjust

Children add and subtract numbers that sit just below a ten, such as 19, 29 or 99. They use the friendly ten instead and then adjust: 47 + 19 is 47 + 20 = 67, take back 1, so 66. When subtracting, taking away too much means adding back.

We are learning to

• round a number like 19 or 39 up to its friendly ten, and say how much was added,
• add the friendly number, then take back the extra,
• subtract the friendly number, then add back the extra.

Success criteria

• I can add and subtract numbers like 29 by rounding and adjusting.
• I can explain whether to take back or add back.

You need

The number cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 64 − 19.

Watch for these ideas

• Adjusting the wrong way when subtracting: 64 − 20 = 44, then take back 1 = 43. Taking away too much means adding back: 45.
• Forgetting how much was added: rounding 48 to 50 is 2 extra, not 1.
• Rounding when it does not help. 47 + 23 is quicker by splitting.

Answers

• Part A: 36 + 20 = 56, take back 1, 55; 47 + 30 = 77, take back 1, 76; 58 + 40 = 98, take back 1, 97; 125 + 100 = 225, take back 1, 224.
• Part B: 64 − 20 = 44, add back 1, 45; 82 − 30 = 52, add back 1, 53; 91 − 50 = 41, add back 2, 43; 150 − 100 = 50, add back 1, 51. Part C: we took away 1 more than 19, so we give it back.

Round, then adjust

A. Add the friendly ten, then take back

B. Take away the friendly ten, then add back

C. For 64 − 19 we took away 20. Why do we add 1 back?

Multiply by parts

Children multiply a two-digit number by a one-digit number in their heads by splitting the two-digit number by place value: 4 × 23 is 4 × 20 = 80 and 4 × 3 = 12, so 92. A rectangle cut into a tens part and a ones part shows why both parts count.

We are learning to

• split a two-digit number into tens and ones to multiply it,
• multiply a multiple of ten by a one-digit number (6 × 40 is 6 × 4 tens),
• add the two part products to get the whole product.

Success criteria

• I can multiply by parts and show it on a split rectangle.
• I can find the mistake when a part has been missed.

You need

The worksheet, one per child. Grid paper for drawing rectangles (optional).

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the rectangle for 4 × 23.

Watch for these ideas

• Multiplying only the tens, or only the ones: 4 × 23 as 80 or as 12. Both parts are multiplied.
• Multiplying the tens digit as ones: 4 × 2 = 8, then 8 + 12 = 20. The 2 is 2 tens.
• Adding the factors: 4 × 23 as 4 + 20 + 3. Draw the rectangle to see the parts.

Answers

• Part A: 3 × 24 = 60 + 12 = 72; 4 × 36 = 120 + 24 = 144; 6 × 15 = 60 + 30 = 90; 5 × 42 = 200 + 10 = 210.
• Part B: 6 × 40 = 240; 8 × 30 = 240; 7 × 50 = 350. Part C: her 4 × 20 = 80 is right, but the ones part 4 × 3 is 12, not 2; 80 + 12 = 92.

Multiply by parts

A. Write a product in each part, then add

B. Tens times

6 × 40 = 6 × 4 tens = ________8 × 30 = 8 × 3 tens = ________7 × 50 = 7 × 5 tens = ________

C. Mia says 4 × 23 = 82. Which part went wrong? Show the right answer.

Divide with a known fact

Children divide when there is no remainder by finding the matching multiplication: 56 ÷ 8 asks what times 8 makes 56. For bigger numbers they split the number being shared into a friendly part and the rest: 88 ÷ 4 is 80 ÷ 4 = 20 and 8 ÷ 4 = 2, so 22.

We are learning to

• use a multiplication fact to divide (because 7 × 8 = 56, 56 ÷ 8 = 7),
• split a two-digit number into a friendly part and the rest to divide it,
• check a division by multiplying back.

Success criteria

• I can divide using the matching times table fact.
• I can split a number to divide it, and check by multiplying.

You need

About 90 counters or paper squares per group for sharing (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 88 ÷ 4.

Watch for these ideas

• Dividing each digit on its own. It happens to work for 84 ÷ 4 (21), but not for 75 ÷ 5: split 75 into 50 and 25 instead.
• Forgetting to add the two part answers: 88 ÷ 4 as 20.
• Not checking. Multiplying back catches most slips.

Answers

• Part A: 48 ÷ 6 = 8; 63 ÷ 7 = 9; 56 ÷ 8 = 7; 45 ÷ 9 = 5.
• Part B: 88 ÷ 4 = 20 + 2 = 22; 69 ÷ 3 = 20 + 3 = 23; 75 ÷ 5 = 10 + 5 = 15; 84 ÷ 7 = 10 + 2 = 12. Part C: 96 ÷ 4 = 24 stickers each.

Divide with a known fact

A. Use the times table fact

B. Split the number being shared

C. A sharing story

Four friends share 96 stickers equally. How many stickers does each friend get?

Number sentence: __________________    Each friend gets ______ stickers.

Pick the strategy

Children look at the numbers before they choose: split for 34 + 52, round and adjust for 65 + 29, parts for 3 × 42, a known fact for 56 ÷ 8. For 4826 + 3975 the efficient tool is a calculator, but only after an estimate, so they can tell if they pressed a wrong key.

We are learning to

• choose a mental strategy that fits the numbers, and say why it fits,
• decide when a calculator is the efficient tool,
• estimate before using a calculator, and check the answer is close.

Success criteria

• I can sort problems by the strategy that suits them and explain my choice.
• I can estimate, use a calculator, and say if the answer makes sense.

You need

The strategy-sort cards (cut-out sheet 2), one set per group of four. A calculator per group. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the card sort; start Session B with Part B.

Watch for these ideas

• Using one strategy for everything, such as always splitting. Ask what in the numbers suggests a shortcut.
• Trusting the calculator without an estimate. A slipped key gives a wrong answer that looks just as sure.
• Reaching for the calculator for 7 × 9. A known fact is faster.

Answers

• Part A: Split into tens and ones: 34 + 52 = 86, 43 + 25 = 68, 61 + 37 = 98. Round, then adjust: 65 + 29 = 94, 91 − 39 = 52, 48 + 99 = 147. Multiply by parts: 3 × 42 = 126, 6 × 27 = 162, 5 × 33 = 165. Use a known fact: 56 ÷ 8 = 7, 7 × 9 = 63, 72 ÷ 9 = 8. Estimate, then use a calculator: 4826 + 3975 = 8801, 9204 − 5768 = 3436, 386 × 7 = 2702. Other choices are fine if the child can say why they fit.
• Part B: 3847 + 2965: about 6800, exactly 6812; 9104 − 4987: about 4100, exactly 4117; 312 × 8: about 2400, exactly 2496. Part C: 39 + 46 = 85; 7 × 28 = 196; 63 ÷ 9 = 7; 6 × 50 = 300.

Pick the strategy

A. Our card sort

B. Estimate first, then use a calculator

C. Choose a strategy and solve

Number cards

Cut out the 24 cards. Partners shuffle them face down, turn over two, and add them (Day 1) or take the smaller from the larger (Day 2) with the strategy of the day. One set per pair.

Teacher note: nine of the cards end in 8 or 9 (such as 19, 29, 99), so most pairs give a chance to round and adjust.

Strategy-sort cards

Cut out the five headers and the fifteen problem cards (Day 5). Lay the headers in a row. Put each problem under the strategy that fits its numbers best, then solve it that way.

Headers

Problem cards

Teacher note: there are three cards for each strategy, and the key is on the Day 5 plan. A child who sorts a card differently and can say why the numbers suit it is right too.

What we know: Efficient Strategies

Work in your head for questions 1 to 7. Show your strategy.

1. Split to add: 46 + 37 = ______ + ______ = __________
2. Round and adjust: 58 + 29 = 58 + ______ = ______, then take back ______ = __________
3. Round and adjust: 74 − 19 = 74 − ______ = ______, then add back ______ = __________
4. Multiply by parts: 5 × 34 = 5 × 30 + 5 × 4 = ______ + ______ = __________
5. 3 × 40 = __________
6. 92 ÷ 4 = __________   Check: ______ × 4 = 92
7. Which strategy would you use for 63 + 29? Why? ______________________________
8. Estimate 4827 + 3958: about ________. Now use a calculator: ________. Is it close to your estimate? ______

Answers and marking guide

Answers

1. 70 + 13 = 83.
2. 58 + 30 = 88, take back 1: 87.
3. 74 − 20 = 54, add back 1: 55.
4. 150 + 20 = 170.
5. 120 (3 × 4 tens = 12 tens).
6. 23; 23 × 4 = 92 (80 ÷ 4 = 20 and 12 ÷ 4 = 3).
7. Round and adjust: 63 + 30 = 93, take back 1 = 92. Splitting is fine with a reason.
8. About 8800 (4800 + 4000); exactly 8785; yes, close.

A quick three-level guide

Eight questions, three ideas. A child at standard gets most answers right in their head and can name the strategy and say why it suits the numbers.

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, rounding and adjusting, parts, facts, and choosing.