Adding and Subtracting Decimals: a week of ready-to-teach maths

Five days of lessons for Year 6 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus twenty decimal cards, twelve price tags, 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 decimal cards and price tags once; one set per pair serves Days 2 to 5.
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 decimal is place value carried on to the right of the ones. Each place is worth a tenth of the place on its left, so decimals add and subtract just like whole numbers, as long as tenths stay under tenths and hundredths under hundredths. Lining up the decimal points does that. An estimate made by rounding says roughly how big the answer must be, which catches a misplaced point before it does harm.

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.

Words to watch

Say 3.45 as “three point four five”, not “three point forty-five”. A zero can hold a place, as in 3.05, or be written at the end without changing the value: 1.2 = 1.20. Calculators come in on Days 4 and 5, always after an estimate, as the descriptor’s digital tool for checking and for long sums.

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 makes sure every digit is read for its place; Day 2 adds with the points in line; Day 3 subtracts, from whole numbers too; Day 4 estimates first and judges every answer; and Day 5 puts it all to work with money and measures. It builds on the Year 5 work of comparing decimals with more than two places and checking answers with estimates. It leads to the next units, multiplying and dividing by powers of 10 and percentages of a quantity, and to Year 7, where decimals are rounded to a given accuracy.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• For Days 4 and 5: a calculator for each pair (a tablet or laptop calculator is fine).
• Cut out once, use all week: the twenty decimal cards and the twelve price tags, one set per pair. No other equipment to buy.

Words for the word wall

decimal point, tenths, hundredths, thousandths, place value, partition, regroup, line up, estimate, round, nearest whole, nearest tenth, reasonable, difference, change

Dear families

This week in maths, Year 6 adds and subtracts decimals. We line up the decimal points so tenths sit under tenths, estimate before every calculation, and check whether each answer makes sense. Money and measurements give us plenty to practise with.

Try this at home

• At the shops or with a receipt, round each price to the nearest dollar and estimate the total. How close was it?
• Work out the change from $20 for something that costs $13.65, by counting up from the price.
• Measure two lengths in metres, such as 1.45 m and 0.8 m. What is the difference?
• Ask: is 4.7 + 2.6 more or less than 7? How do you know without working it out?

My decimals this week

Fill one row a day. Find two decimals at home (prices, lengths, times), add them and take one from the other.

Printed from the free seegongsik Adding and Subtracting Decimals teaching pack · seegongsik.com/au/y6/number/AC9M6N04/pack

Every digit in its place

Each place to the right of the decimal point is worth a tenth of the place on its left: tenths, hundredths, thousandths. Children read and build decimals on a place-value chart, partition them, and add or take away one tenth, hundredth or thousandth by changing one digit.

We are learning to

• read and write decimals to thousandths and name the value of each digit,
• partition a decimal by place value,
• add or take away 0.1, 0.01 or 0.001, including when a digit rolls over.

Success criteria

• I can say what the 4 is worth in 0.43 and in 2.054.
• I can add 0.01 to 2.99 and explain which digits change.

You need

The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the 4s in Part C.

Watch for these ideas

• Longer means larger: 3.054 is less than 3.45, because 0 tenths is less than 4 tenths.
• Reading 3.45 as “three point forty-five”. Say “three point four five”.
• Adding 0.01 by writing a 1 on the end: 2.35 + 0.01 is 2.36, not 2.351.

Answers

• Part A: each digit under its place name; 0.006 has 0 ones, 0 tenths, 0 hundredths and 6 thousandths.
• Part B: 3.45 = 3 + 0.4 + 0.05; 12.08 = 10 + 2 + 0.08; 0.736 = 0.7 + 0.03 + 0.006; 5.207 = 5 + 0.2 + 0.007.
• Part C: 4.1: 4; 0.43: 0.4; 2.054: 0.004; 1.64: 0.04.
• Part D: 2.35 + 0.1 = 2.45; 2.35 + 0.01 = 2.36; 4.7 − 0.1 = 4.6; 2.99 + 0.01 = 3.00; 5.0 − 0.01 = 4.99; 1.999 + 0.001 = 2.000.
• Part E: 3.054 < 3.405 < 3.45 < 3.5.

Every digit in its place

A. Write each number in the chart

B. Split each number by place value

C. What is the 4 worth?

D. Nudge one place

E. Smallest first

3.45, 3.054, 3.5, 3.405

________  <  ________  <  ________  <  ________

Line up the points

Adding decimals is adding whole numbers with the places kept straight. Line up the decimal points so tenths sit under tenths, fill an empty place with a zero if it helps, and regroup ten of a place as one of the place on its left, across the point too.

We are learning to

• set out a decimal addition in columns with the points in line,
• add with regrouping, including ten tenths into one whole,
• estimate first, then check the total against the estimate.

Success criteria

• I can work out 1.2 + 0.35 and explain where each digit goes.
• I can regroup 11 tenths as 1 whole and 1 tenth.

You need

The worksheet, one per child, and the cut-out decimal cards, one set per pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the addition vote on the board.

Watch for these ideas

• Lining up the last digits instead of the points: 1.2 + 0.35 becomes 0.47.
• Writing 11 in the tenths column. Ten tenths make one whole, which moves into the ones.
• Dropping the point from the answer. It sits under the points above it.

Answers

• Part A: 1.2 + 0.35 = 1.55; 2.4 + 1.7 = 4.1; 0.85 + 0.15 = 1.00; 3.06 + 2.8 = 5.86.
• Part B: 4.6 + 2.75 = 7.35; 0.9 + 0.08 = 0.98; 12.5 + 3.75 = 16.25; 6.48 + 1.52 = 8.00.
• Part C: 4 + 4 = 8, exact 8.1; 7 + 2 = 9, exact 9.03.
• Part D: Jai lined up the last digits, 2 under 5, and added 12 and 35 hundredths. With the points in line, 1.2 + 0.35 = 1.55.

Line up the points

A. Add in the columns

Tens, ones, point, tenths, hundredths: each digit already sits in its place.

B. Set them out yourself, then add

C. Estimate, then add

3.9 + 4.2: about ______ + ______ = ______    exact ________

7.05 + 1.98: about ______ + ______ = ______    exact ________

D. What did Jai do?

Jai wrote 1.2 + 0.35 = 0.47. What did Jai do? What is the right answer?

______________________________________________________________________

Take it away

Subtraction works the same way: points in a line, then subtract place by place, regrouping one of a place as ten of the place on its right when the top digit is too small. A whole number gets a point and zeros so every place has a digit, and adding the answer back checks it.

We are learning to

• subtract decimals in columns with the points in line,
• subtract a decimal from a whole number by writing in the zeros,
• check a subtraction by adding the answer back.

Success criteria

• I can work out 8 − 3.45 and 10.2 − 4.67.
• I can check a subtraction by adding, and fix it if it is wrong.

You need

The worksheet, one per child, and the cut-out decimal cards, one set per pair.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Taking the smaller digit from the larger, whichever row it is in. In 6.30 − 2.85 the hundredths are 0 take away 5: regroup a tenth first.
• Leaving the whole number as it is: 8 − 3.45 needs 8.00, so every place of 3.45 has a digit above it.
• Forgetting to check. Adding the answer back must give the top number.

Answers

• Part A: 3.8 − 1.5 = 2.3; 5.0 − 2.4 = 2.6; 1.25 − 0.75 = 0.50; 6.3 − 2.85 = 3.45.
• Part B: 8 − 3.45 = 4.55; 10.2 − 4.67 = 5.53; 7.5 − 0.68 = 6.82; 12 − 0.9 = 11.1.
• Part C: 9.4 − 3.7 = 5.7 is right (5.7 + 3.7 = 9.4). 4.05 − 1.6 = 3.45 is wrong; it is 2.45. 6.2 − 0.85 = 5.45 is wrong; it is 5.35. 7 − 2.3 = 4.7 is right (4.7 + 2.3 = 7.0).
• Part D: 1.75 L is left; Ella jumped 0.45 m further.

Take it away

A. Subtract in the columns

B. Set them out yourself, then subtract

C. Check by adding back. Tick it, or fix it.

D. Measures

1. A jug holds 2.5 L of juice. Then 0.75 L is poured out. How much is left? ____________

2. Ella jumped 3.42 m and Kai jumped 2.97 m. How much further did Ella jump? ____________

Estimate first

Rounding each number to the nearest whole, or tenth, gives an estimate in the head. Children estimate before every calculation, calculate on paper or with a calculator, and use the estimate to judge whether the answer is reasonable, above all whether the point is in the right place.

We are learning to

• round decimals to the nearest whole number and the nearest tenth,
• estimate a sum or difference before calculating it,
• judge whether an answer is reasonable, and find the slip when it is not.

Success criteria

• I can estimate 6.8 + 2.95 in my head.
• I can spot an answer with the point in the wrong place and say what it should be.

You need

The worksheet, one per child, and a calculator for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the first line of Part B.

Watch for these ideas

• Rounding 7.25 down to 7.2. A 5 in the next place rounds up: 7.3.
• Trusting the calculator over the estimate. A missed point on the keys gives an answer ten times out.
• Rounding to a whole when the numbers are less than 1. Round to tenths instead.

Answers

• Part A, nearest whole and nearest tenth: 4.83: 5, 4.8; 7.25: 7, 7.3; 0.96: 1, 1.0; 12.47: 12, 12.5; 3.05: 3, 3.1.
• Part B: 6.8 + 2.95: about 10, exact 9.75; 12.4 − 3.86: about 8, exact 8.54; 0.48 + 0.39: about 0.9, exact 0.87; 25.1 − 9.75: about 15, exact 15.35.
• Part C: 33 is not (about 3; it is 3.3); 8.15 is reasonable; 6.23 is reasonable; 0.13 is not (about 2; it is 1.3); 82.5 is not (about 9; it is 8.25).
• Part D: about 25; the calculator gives 24.40.

Estimate first

A. Round each number

B. Estimate, calculate, check

C. Reasonable or not?

Estimate each one. Tick the reasonable answers. For the others, write the right answer.

D. A calculator sum

Estimate first, then use a calculator: 3.75 + 12.6 + 0.85 + 7.2

Estimate ________    Calculator ________    Does it make sense? ________

The corner shop

Money and measures are decimals at work. Children total a shopping list, work out change, compare two baskets and order race times, choosing to calculate in their heads, on paper or with a calculator, and checking every answer with an estimate.

We are learning to

• add and subtract amounts of money and measures,
• choose a way to calculate: in the head, on paper or with a calculator,
• check each answer with an estimate.

Success criteria

• I can work out the change from $20 by counting up or by subtracting.
• I can say whether my answer makes sense, and why.

You need

The worksheet, one per child, the cut-out price tags, one set per pair, and a calculator for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with a round of Corner shop.

Watch for these ideas

• Writing $1.5 for one dollar fifty. Money always has two places: $1.50.
• Thinking the biggest time won. In a race the smallest time is the fastest.
• Subtracting the wrong way round for change: the note comes first, $20 − total.

Answers

• Part A: total $18.50; change from $20: $1.50.
• Part B: basket A $13.35, basket B $12.43; basket A costs $0.92 more.
• Part C: fastest first, Mia 14.62 s, Raj 14.75 s, Ana 14.9 s, Leo 15.08 s; the gap from first to last is 0.46 s.
• Part D: partners check each other’s problem with an estimate and a calculator.

The corner shop

A. A shopping list

Estimate first: about ________.   Paid with a $20 note. Change: ________

B. Which basket costs more?

Basket ______ costs more, by ________.

C. The 100 m race

Mia 14.62 s, Leo 15.08 s, Ana 14.9 s, Raj 14.75 s

Fastest first: ______________________________   Gap from first to last: ________

D. Your own shop problem

Choose two price tags. Write a problem for a partner that needs an addition and a subtraction. Estimate the answer first.

______________________________________________________________________

______________________________________________________________________

Decimal cards

Cut out the twenty cards once. Pairs use them on Days 2 to 4.

Close to 5 (Days 2 to 4)

1. Shuffle the cards face down. Each player turns over three cards.
2. Choose two of your three to add as close to 5 as you can. Estimate first, then add on paper.
3. Your score is the difference between your total and 5: subtract the smaller from the larger.
4. After five rounds, add up your scores. The lower total wins.

Teacher note: these pairs make 5 exactly, a score of 0: 0.5 + 4.5, 0.65 + 4.35, 1.2 + 3.8, 1.75 + 3.25, 2.3 + 2.7, 2.48 + 2.52.

Price tags

Cut out the twelve tags once, one set for each pair.

Corner shop (Day 5)

1. The shopkeeper lays out the tags. The shopper has $20 and picks four items.
2. The shopper estimates the total, then adds on paper.
3. The shopkeeper checks the total on a calculator, then counts up the change to $20.
4. Over $20? Swap one item for a cheaper one and try again. Then swap jobs.

Teacher note: four tags cost from $8.50 (the four cheapest) to $24.10 (the four dearest), so some baskets fit the $20 and some do not.

What we know: Adding and Subtracting Decimals

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

1. What is the 7 worth in 3.475? ________
2. 4.6 + 2.75 = ________
3. 8 − 3.45 = ________
4. 12.3 − 4.86 = ________
5. Estimate 6.8 + 2.95 by rounding each number to the nearest whole. ________
6. Is 5.2 − 1.9 = 33 reasonable? Why? ______________________________
7. Lily says 0.5 + 0.25 = 0.30. Explain the mistake and give the right answer. ______________________________
8. A $20 note pays for two items costing $6.45 and $8.90. How much change? ________

Set out questions 2, 3 and 4 here.

Answers and marking guide

Answers

1. 7 hundredths, 0.07.
2. 7.35.
3. 4.55 (write 8 as 8.00).
4. 7.44.
5. 7 + 3 = 10 (exact 9.75).
6. No: 5 − 2 = 3, so 33 is far too big; it is 3.3.
7. Lily added 5 and 25 as if they were the same kind of piece. With the points in line, 0.50 + 0.25 = 0.75.
8. $4.65 (the items cost $15.35).

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, with the points in line, an estimate or a check by adding back.

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: place value, adding with the points in line, subtracting, estimating first, and money and measures.