Mental Strategies from Facts: a week of ready-to-teach maths

Five days of lessons for Year 3 Algebra. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus make-ten cards, strategy 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 make-ten cards and the strategy cards once; they 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. Mental maths rests on the facts to 20 and on place value: 7 + 6 = 13 also tells you 47 + 6 = 53 and 70 + 60 = 130. The week builds four ways to add and subtract two-digit numbers in your head (make a ten, partition, jump, round and adjust) and one way to subtract when the ones run short. No calculators.

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.

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

Day 1 starts from the facts to 20 and shows how they grow into bigger sums. Days 2 to 4 each add a strategy for two-digit addition. Day 5 adds subtraction with regrouping and asks children to choose the strategy that suits the numbers. It leans on Addition and Subtraction Undo Each Other (AC9M3A01) and Add and Subtract to Three Digits (AC9M3N03).

Materials for the week (one trip)

• From the classroom: scissors, pencils, mini whiteboards or scrap paper, this pack printed.
• Base-ten blocks (tens rods and ones) and a few ten frames with counters.
• A hundred chart and a 0 to 100 number line or bead string for the board.
• Cut out once, use all week: the make-ten cards and the strategy cards in this pack.

Words for the word wall

make ten, bridge, partition, tens, ones, jump, empty number line, round, adjust, take back, regroup, open a ten, strategy, mental

Dear families

This week in maths, Year 3 is learning to add and subtract two-digit numbers in their heads, by building on the facts to 20 they already know.

Try this at home

• Play “ten pairs”: say a number to 10 and your child says its partner (7 and 3).
• Ask for a sum and then a bigger cousin: 8 + 5 = 13, so what is 28 + 5? And 80 + 50?
• Add 9 the quick way: add 10, then take 1 back (34 + 9 = 44 − 1 = 43).
• Ask how they worked a sum out. There is usually more than one good way.

Our mental maths this week

Fill one row a day: a sum, the answer, and how you worked it out in your head.

Printed from the free seegongsik Mental Strategies from Facts teaching pack · seegongsik.com/au/y3/algebra/AC9M3A02/pack

Make a ten first

Facts to 20 are the building blocks of mental maths. Adding works in any order, so look for a pair that makes ten: 8 + 5 + 2 is 8 + 2 = 10, then 10 + 5 = 15. A fact you know also grows: 8 + 5 = 13 tells you 38 + 5 = 43.

We are learning to

• recall the pairs that make ten and use them to add three numbers,
• bridge through ten (8 + 5 is 8 + 2 + 3),
• use a fact to 20 with larger numbers (8 + 5 = 13, so 38 + 5 = 43 and 80 + 50 = 130).

Success criteria

• I can find a pair that makes ten.
• I can use a fact I know with bigger numbers.

You need

The make-ten cards (cut-out sheet 1), one set per pair. Ten frames and counters. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the chains; start Session B with Bridge through ten.

Watch for these ideas

• Adding left to right every time (8 + 5, then + 2). Look for the ten first.
• Losing the third number after making the ten. Write the ten, then add what is left.
• Not seeing 38 + 5 as 8 + 5 with 30 more. The ones fact is the same; only the tens grow.

Answers

• Chains: (6 + 4) + 7 = 10 + 7 = 17; (9 + 1) + 3 = 10 + 3 = 13; (5 + 5) + 8 = 10 + 8 = 18; (2 + 8) + 6 = 10 + 6 = 16; (7 + 3) + 9 = 10 + 9 = 19; (12 + 8) + 5 = 20 + 5 = 25.
• Bridges: 8 + 2 + 4 = 14; 9 + 1 + 4 = 14; 7 + 3 + 2 = 12; 6 + 4 + 3 = 13.
• Grow: 7 + 5 = 12, so 27 + 5 = 32, 47 + 5 = 52 and 70 + 50 = 120; 9 + 6 = 15, so 29 + 6 = 35, 49 + 6 = 55 and 90 + 60 = 150.

Make a ten first

Make the ten first

Circle two numbers that make a ten (or a twenty). Add them first, then add the last number.

Bridge through ten

Example: 8 + 5 = 8 + 2 + 3 = 13. Split the second number to make a ten first.

Grow the fact

7 + 5 = 12, so   27 + 5 = ______    47 + 5 = ______    70 + 50 = ______

9 + 6 = 15, so   29 + 6 = ______    49 + 6 = ______    90 + 60 = ______

Partition to add

Split both numbers into tens and ones, add each place, then put them together: 47 + 36 is 40 + 30 = 70 and 7 + 6 = 13, so 70 + 13 = 83. The ones use a fact to 20.

We are learning to

• partition two-digit numbers into tens and ones,
• add the tens, add the ones, then combine the two,
• regroup when the ones make 10 or more (13 ones is 1 ten and 3 ones).

Success criteria

• I can add two-digit numbers by partitioning.
• I can combine the tens and ones when the ones make 10 or more.

You need

Base-ten blocks (tens rods and ones) for each pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the board; start Session B with the worksheet.

Watch for these ideas

• Adding the tens digits as ones (4 + 3 = 7). The 4 in 47 is 40.
• Writing 70 and 13 side by side as 713. 13 ones is 1 ten and 3 ones, so 70 + 13 = 83.
• Adding only the tens or only the ones. Both places need adding.

Answers

• 35 + 42 = 70 + 7 = 77; 46 + 27 = 60 + 13 = 73; 58 + 34 = 80 + 12 = 92; 29 + 45 = 60 + 14 = 74; 63 + 19 = 70 + 12 = 82; 37 + 56 = 80 + 13 = 93.
• Story: 46 + 38 = 70 + 14 = 84 books.
• In your head: 59, 79 and 81.

Partition to add

Split and add

Example: 47 + 36. Tens: 40 + 30 = 70. Ones: 7 + 6 = 13. Together: 70 + 13 = 83.

Story

The library has 46 picture books and 38 chapter books. How many books is that altogether? Show how you split the numbers.

Tens: ______________   Ones: ______________   Together: ______________

Jump by place

Keep the first number whole and jump along an empty number line: tens first, then ones. 56 + 27 is 56 + 20 = 76, then 76 + 7 = 83. Only one number is held in your head at a time.

We are learning to

• keep the first number whole and count on by the tens, then the ones,
• draw the jumps on an empty number line,
• split a ones jump to land on a ten when that helps (76 + 7 = 76 + 4 + 3).

Success criteria

• I can add by jumping the tens, then the ones.
• I can draw my jumps on an empty number line.

You need

A 0 to 100 bead string or number line for the board. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the board; start Session B with the worksheet and Two ways.

Watch for these ideas

• Jumping 2 instead of 20 for the tens of 27. The 2 is 2 tens.
• Starting the jumps at 0. Start at the first number and keep it whole.
• Jumping the ones in ones and losing count. Jump to the next ten, then the rest.

Answers

• Number lines: 45 + 30 = 75, then + 2 = 77; 38 + 20 = 58, then + 6 = 64; 57 + 30 = 87, then + 5 = 92; 64 + 20 = 84, then + 9 = 93.
• In your head: 29 + 40 = 69, then + 3 = 72; 46 + 30 = 76, then + 7 = 83.
• Two ways: 40 + 30 = 70 and 8 + 5 = 13, so 83; or 48 + 30 = 78, then + 5 = 83.

Jump by place

Start at the first number. Draw a jump for the tens, then a jump for the ones. Write where you land.

Jump in your head

29 + 43   tens jump to ______, ones jump to ______

46 + 37   tens jump to ______, ones jump to ______

Round and adjust

When a number is close to a ten, round it, add, then adjust: 47 + 39 is 47 + 40 = 87, but that added 1 too many, so 87 − 1 = 86. Adding 9, 19, 29 or 39 becomes quick this way.

We are learning to

• round a number that is close to a ten (39 up to 40),
• add the friendly number, then adjust by what was changed,
• decide whether to take back or add back (rounding up when adding means take back).

Success criteria

• I can add by rounding and adjusting.
• I can say whether to take back or add back, and how much.

You need

A hundred chart for the board. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the additions; start Session B with the take-aways and Does it help?

Watch for these ideas

• Adjusting the wrong way (87 + 1 = 88). Rounding up added too much, so take back.
• Taking back the wrong amount (taking back 9). Take back only the extra: 40 is 1 more than 39.
• Rounding numbers far from a ten (34 up to 40, take back 6). Use another strategy.

Answers

• 35 + 20 − 1 = 54; 46 + 30 − 1 = 75; 58 + 40 − 1 = 97; 27 + 50 − 2 = 75; 63 + 20 − 2 = 81; 44 + 40 − 2 = 82.
• Take-aways: 52 − 20 + 1 = 33; 75 − 30 + 1 = 46 (taking away too much, so add back).
• Does it help? Yes for 36 + 29 and 55 + 18 (65, 73); no for 41 + 32 and 62 + 25 (73, 87).

Round and adjust

Round, add, then take back

Example: 47 + 39 = 47 + 40 − 1 = 86.

Try it on a take-away

Take away the friendly number. You took away too much, so add back.

52 − 19 = 52 − ______ + ______ = ______

75 − 29 = 75 − ______ + ______ = ______

Regroup and choose

When the ones run short in a take-away, open a ten: 63 − 28 has only 3 ones, so 63 becomes 50 and 13. Then 13 − 8 = 5 and 50 − 20 = 30, so the answer is 35. Each strategy this week suits some numbers better than others.

We are learning to

• open a ten into ten ones when the ones run short,
• take away the ones, then the tens,
• choose a strategy that suits the numbers and say why it fits.

Success criteria

• I can take away by opening a ten.
• I can choose a strategy and say why it fits.

You need

Base-ten blocks. The strategy cards (cut-out sheet 2), one set per pair. The worksheet. The unit’s self-check quiz.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the take-aways; start Session B with the choices, the cards and the quiz.

Watch for these ideas

• Taking the smaller ones digit from the bigger (8 − 3 = 5, so 45). Open a ten instead.
• Forgetting that a ten has gone (63 becomes 60 and 13). Opening a ten leaves 50.
• Using one strategy for everything. Look at the numbers first, then choose.

Answers

• 52 = 40 + 12; 12 − 7 = 5; 40 − 20 = 20; so 25. 74 = 60 + 14; 14 − 8 = 6; 60 − 30 = 30; so 36. 61 = 50 + 11; 11 − 4 = 7; 50 − 20 = 30; so 37.
• 85 = 70 + 15; 15 − 7 = 8; 70 − 40 = 30; so 38. 93 = 80 + 13; 13 − 8 = 5; 80 − 50 = 30; so 35. 46 = 30 + 16; 16 − 8 = 8; 30 − 10 = 20; so 28.
• Choices: 38 + 19 = 57, by round and adjust (38 + 20 − 1); 45 + 32 = 77, by partition, or jump by place (70 + 7); 64 − 30 = 34, by just take the tens (6 tens − 3 tens). Other sensible choices are fine if children can say why.

Regroup and choose

Open a ten to take away

Example: 63 − 28. 63 = 50 + 13. Ones: 13 − 8 = 5. Tens: 50 − 20 = 30. Answer: 35.

Choose a strategy

Choose a strategy from this week, solve it, and say why it suits the numbers.

Make-ten cards

Cut out the twenty cards. On Day 1, flash a card and the class calls its partner to ten. For make-ten memory, lay the cards face down; a pair turns two over and keeps them if they make ten.

Teacher note: the deck holds two of each pair, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, so every card has a partner.

Strategy cards

Cut out the twelve cards. On Day 5, pairs sort them by the strategy that suits the numbers best (make a ten, partition, jump by place, round and adjust, open a ten, or just the tens), then solve each one in their heads.

Teacher note, a strategy that suits each card (others can work too, if children can say why): 43 + 25 = 68 (partition), 57 + 29 = 86 (round and adjust), 66 + 27 = 93 (jump by place), 82 − 37 = 45 (open a ten), 50 + 40 = 90 (just the tens), 34 + 49 = 83 (round and adjust), 75 − 42 = 33 (partition), 61 − 26 = 35 (open a ten), 7 + 5 + 3 = 15 (make a ten), 48 + 36 = 84 (partition or jump), 90 − 60 = 30 (just the tens), 25 + 39 = 64 (round and adjust).

What we know: Mental Strategies from Facts

Work on your own, in your head. Write down the steps you used.

1. Make a ten first: 7 + 8 + 3 = ______________________
2. 6 + 7 = 13, so 46 + 7 = ______ and 60 + 70 = ______
3. Partition: 38 + 45 = ______ + ______ = ______
4. Jump: 52 + 36. Jump the tens to ______, then the ones to ______.
5. Round and adjust: 45 + 39 = 45 + 40 − ______ = ______
6. Open a ten: 71 − 36 = ______________________
7. Which strategy would you use for 66 + 19? Why? ______________________________ Answer: ______
8. There were 91 people at the pool and 47 went home. How many are still at the pool? ______

Answers and marking guide

Answers

1. (7 + 3) + 8 = 10 + 8 = 18.
2. 53 and 130.
3. 70 + 13 = 83.
4. 82, then 88.
5. 1; 84.
6. 71 = 60 + 11; 11 − 6 = 5; 60 − 30 = 30; so 35.
7. Round and adjust, because 19 is close to 20: 66 + 20 − 1 = 85. (Jumping is fine too.)
8. 44 (91 = 80 + 11; 11 − 7 = 4; 80 − 40 = 40).

A quick three-level guide

Eight questions, three ideas. A child at standard solves each one in their head and can say the steps; the written steps matter more than speed.

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: making a ten, partitioning, jumping by place, rounding and adjusting, and regrouping and choosing.