Adding and Subtracting Fractions: 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 a cut-out fraction wall and story 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 fraction wall and the story 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. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: fractions can be added or taken away when their parts are the same size. Then add or subtract the numerators and keep the denominator, because the size of the parts does not change: 3/8 + 2/8 = 5/8, never 5/16. When one denominator is a multiple of the other, rename one fraction first: 1/2 + 1/4 is 2/4 + 1/4 = 3/4.

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.

Answers that simplify

An answer such as 3/6 is correct as it stands. Where it simplifies, the answers also give the simplest form, 3/6 = 1/2, so children can meet it on Day 5 without being marked down before then. Sums stay at one whole or less, apart from the bigger challenges.

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 add and subtract parts of the same size; Days 3 and 4 rename one fraction so the parts match, then add or subtract; and Day 5 solves stories three ways and tidies the answers. It builds on this year’s equivalent and related-denominator fractions (AC9M5N03), and it leads to Year 6, where fractions are added and subtracted with equivalent fractions and the denominators need not be related.

Materials for the week (one trip)

• From the classroom: scissors, coloured pencils (two colours each), envelopes for the cards, this pack printed.
• For Day 5: a classroom clock, or a clock face drawn on the board.
• Cut out once, use all week: the fraction wall and the eight story cards in this pack. No maths equipment to buy.

Words for the word wall

numerator, denominator, same denominator, related denominators, rename, equivalent, sum, difference, whole, simplify, strategy

Dear families

This week in maths, Year 5 adds and subtracts fractions. When the parts are the same size we add or subtract the numerators and keep the denominator: 3/8 + 2/8 = 5/8. When the denominators are related, we rename one fraction first: 1/2 + 1/4 = 2/4 + 1/4 = 3/4.

Try this at home

• Cut a pizza or a sandwich into eighths. Eat 3/8 and share 2/8: how much is gone, and how much is left?
• Use a clock: half an hour and a quarter of an hour make how many minutes? What fraction of an hour is that?
• Pour 3/4 of a cup of water, then pour out 1/2 a cup. How much is left?
• Ask your child to explain why 3/8 + 2/8 is not 5/16.

My fraction sums this week

Fill one row a day. Make up a fraction sum or difference from home.

Printed from the free seegongsik Adding and Subtracting Fractions teaching pack · seegongsik.com/au/y5/number/AC9M5N05/pack

Add parts of the same size

Children add fractions whose parts are the same size: three eighths and two eighths are five eighths, so they add the numerators and keep the denominator. Bars in two colours show why the denominator does not change.

We are learning to

• add fractions with the same denominator by adding the numerators,
• explain why the denominator stays the same when we add,
• solve a story problem with a bar, including how much is left of the whole.

Success criteria

• I can add 3/10 + 4/10 and show it on a bar.
• I can explain why 3/8 + 2/8 is not 5/16.

You need

The fraction wall (cut-out sheet 1), one per pair, cut into strips. Two colours of pencil per child. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by adding on the eighths strip.

Watch for these ideas

• Adding the denominators too, so 3/8 + 2/8 = 5/16. The parts are eighths before and after.
• Thinking the denominator counts the shaded parts. It tells the size of each part: the whole is cut into that many.
• Not seeing 10/10 as one whole. When the numerator and denominator match, the whole is full.

Answers

• Part A: 5/8, 3/4, 7/10. Part B: 4/5, 7/10, 5/6, 11/12, 6/8 (= 3/4), 7/9.
• Part C: 4/8, 3/6, 6/10. Part D: 5/8 eaten; 3/8 left.

Add parts of the same size

A. Colour the first fraction, then the second in another colour

B. Add

2/5 + 2/5 = ______3/10 + 4/10 = ______1/6 + 4/6 = ______5/12 + 6/12 = ______3/8 + 3/8 = ______2/9 + 5/9 = ______

C. Find the missing fraction

3/8 + ______ = 7/8______ + 2/6 = 5/64/10 + ______ = 1

D. Pizza for two

Ella ate 2/8 of a pizza and Sam ate 3/8 of the same pizza. How much of the pizza did they eat altogether? How much is left?

Eaten: __________    Left: __________

Take parts of the same size away

Children subtract fractions with the same denominator: they take parts away and count the parts that are left, keeping the denominator. They take a fraction from one whole by naming the whole in the same parts (1 = 8/8), and check by adding back.

We are learning to

• subtract fractions with the same denominator by subtracting the numerators,
• take a fraction away from one whole by writing the whole in the same parts,
• check a subtraction by adding the answer back.

Success criteria

• I can work out 11/12 − 4/12 and show it on a bar.
• I can work out 1 − 3/8.

You need

The fraction wall strips from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 5/8 − 5/8.

Watch for these ideas

• Subtracting the denominators too, so 5/6 − 2/6 = 3/0. The parts are still sixths.
• Thinking 1 − 3/8 cannot be done because 1 has no eighths. One whole is 8/8.
• Writing 5/8 − 5/8 = 0/8 and thinking it is unfinished. 0/8 is 0: nothing is left.

Answers

• Part A: 4/8 (= 1/2), 4/6 (= 2/3), 5/10 (= 1/2). Part B: 5/9, 0, 7/12, 1/5, 3/10, 5/7.
• Part C: 5/8, 3/5, 5/12. Part D: 5/10 (= 1/2) of a metre is left; check: 5/10 + 4/10 = 9/10.

Take parts of the same size away

A. Shade the first fraction, then cross out the parts taken away

B. Subtract

7/9 − 2/9 = ______5/8 − 5/8 = ______11/12 − 4/12 = ______4/5 − 3/5 = ______9/10 − 6/10 = ______6/7 − 1/7 = ______

C. Take it away from one whole

1 − 3/8 = ______1 − 2/5 = ______1 − 7/12 = ______

D. The ribbon

A ribbon is 9/10 of a metre long. Mia cuts off 4/10 of a metre. How much ribbon is left? __________

Check by adding back: ______ + ______ = ______

Rename, then add

Children add fractions with related denominators: they rename one fraction so both are counted in the same parts, then add the numerators. On the fraction wall, 1/2 and 2/4 are the same length, so renaming does not change the sum.

We are learning to

• find the larger denominator and rename the other fraction over it,
• add fractions with related denominators,
• check a sum with fraction strips.

Success criteria

• I can work out 1/2 + 1/8 by renaming 1/2 as 4/8.
• I can solve Tom’s walking problem and show my renaming.

You need

The fraction wall strips. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by modelling 2/3 + 1/12.

Watch for these ideas

• Adding tops and bottoms, so 1/2 + 1/4 = 2/6. Rename first: the parts must match.
• Renaming only the denominator, so 1/2 becomes 1/4. Multiply the top as well: 2/4.
• Renaming the fraction with the larger denominator. Rename the one with the smaller denominator.

Answers

• Part A: 3/8, 3/6 (= 1/2). Part B: 4/8 + 1/8 = 5/8; 9/12 + 1/12 = 10/12 (= 5/6); 2/8 + 3/8 = 5/8; 3/10 + 4/10 = 7/10; 3/9 + 2/9 = 5/9; 3/6 + 1/6 = 4/6 (= 2/3).
• Part C: 5/10 + 3/10 = 8/10 (= 4/5) of a kilometre. Part D: 7/8 and 7/8, the same; 3/6 (= 1/2) and 3/8, different.

Rename, then add

A. Lay the strips end to end, then write the sum

1/4 + 1/8 = ______1/3 + 1/6 = ______

B. Rename one fraction, then add

C. Tom’s walk

Tom walked 1/2 of a kilometre to the park, then 3/10 of a kilometre to the shop. How far did he walk altogether?

______ + ______ = ______ of a kilometre

D. Same amount or different? Rename, add, then circle.

1/2 + 3/8   and   3/4 + 1/8     same / different

1/3 + 1/6   and   1/4 + 1/8     same / different

Rename, then take away

Children subtract fractions with related denominators the same way they added: rename one fraction so the parts match, then subtract the numerators. They solve two-step problems and stories, and check by adding back.

We are learning to

• rename one fraction so the denominators match, then subtract,
• solve a two-step problem with related fractions, one step at a time,
• check a subtraction by adding the answer back.

Success criteria

• I can work out 11/12 − 1/3.
• I can find how much cake is left after two slices are eaten.

You need

The fraction wall strips. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the two-step problems.

Watch for these ideas

• Subtracting tops and bottoms, so 5/6 − 1/3 = 4/3. Rename first.
• Renaming, then subtracting the old numerator (5/6 − 1/6). Use the renamed fraction, 2/6.
• Forgetting the whole in a cake problem. One whole cake is 12/12.

Answers

• Part A: 6/8 − 3/8 = 3/8; 5/6 − 3/6 = 2/6 (= 1/3); 7/10 − 2/10 = 5/10 (= 1/2); 11/12 − 4/12 = 7/12; 4/8 − 1/8 = 3/8; 8/9 − 6/9 = 2/9.
• Part B: 3/4, then 5/8; 2/3, then 3/6 (= 1/2). Part C: 1/4 of a litre; 2/3 after lunch, then 3/12 (= 1/4) of the cake is left. Part D: each answer plus the part taken away gives back the first fraction.

Rename, then take away

A. Rename one fraction, then subtract

B. Two steps

1/2 + 1/4 − 1/8   First step: ______   Answer: ______

1 − 1/3 − 1/6   First step: ______   Answer: ______

C. Stories

A jug holds 3/4 of a litre of juice. Ben pours out 1/2 a litre. How much juice is left? __________

A cake was cut into twelfths. At lunch 1/3 of the cake was eaten, and after dinner 5/12 more. How much of the cake is left? __________

D. Check by adding back

Choose two answers from Part A. Add each answer to the fraction taken away. Do you get the first fraction?

______ + ______ = ______     ______ + ______ = ______

Three ways to one answer

Children solve fraction stories with the strategy that fits: a bar cut into equal parts, jumps on a number line, or minutes on a clock for fractions of an hour. Every strategy gives the same answer, and answers are simplified where they can be. The week ends with the unit quiz.

We are learning to

• solve one problem with a bar, a number line and a clock, and get the same answer,
• choose a strategy that fits a story,
• simplify an answer, such as 3/6 = 1/2.

Success criteria

• I can show 1/4 + 1/2 of an hour three ways.
• I can solve a story card and explain my strategy.

You need

The story cards (cut-out sheet 2), two per group. A classroom clock. The worksheet. The interactive unit open for the quiz game.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Expecting each strategy to give a different answer. Every correct strategy lands on the same answer.
• Calling a quarter of an hour 25 minutes. An hour is 60 minutes, so a quarter is 15.
• Simplifying by taking away, so 3/6 becomes 1/4. Divide the top and bottom by the same number: 3/6 = 1/2.

Answers

• Part A: 3/4 of an hour, 15 + 30 = 45 minutes. Part B: 5/6 of an hour (50 minutes); 2/6 (= 1/3) full. Part C: 3/6 = 1/2, 4/8 = 1/2, 6/8 = 3/4, 9/12 = 3/4, 2/6 = 1/3, 5/10 = 1/2.
• Story cards: A 5/8; B 3/6 (= 1/2); C 3/4; D 3/10; E 5/6; F 5/12; G 3/8; H 3/6 (= 1/2).

Three ways to one answer

A. One problem, three ways

Ada read for 1/4 of an hour before school and 1/2 an hour after school. How long did she read?

1/4 + 1/2 = ______ of an hour = ______ minutes

B. Choose a strategy

Max played for 2/3 of an hour, then 1/6 of an hour more. How long did he play?   __________

A tank was 5/6 full. Then 1/2 of the tank was used. How full is it now?   __________

C. Simplify

3/6 = ______4/8 = ______6/8 = ______9/12 = ______2/6 = ______5/10 = ______

D. Our story cards

Card ______   Our answer: __________   Our strategy: ____________________

Card ______   Our answer: __________   Our strategy: ____________________

The fraction wall

Each strip is one whole, the same length. Cut the strips apart, one set per pair, and lay pieces end to end to add, or cover pieces to take away. Pieces that line up exactly name the same amount: 1/2 lines up with 2/4 and with 4/8.

Teacher note: the strips come in three families. Quarters and eighths line up with the halves; sixths, ninths and twelfths line up with the thirds; tenths line up with the fifths. Every renaming in the pack happens inside one family.

Story cards

Cut out the eight cards. Each group solves two cards, chooses a strategy that suits the story, and simplifies the answer if it can.

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

What we know: Adding and Subtracting Fractions

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

1. 4/9 + 3/9 = __________
2. 7/8 − 2/8 = __________
3. 1 − 3/10 = __________
4. 1/2 + 3/8 = __________
5. 5/6 − 2/3 = __________
6. 3/5 + 1/10 = __________
7. Ava ran 3/4 of a kilometre and then walked 1/8 of a kilometre. How far did she go altogether?   __________
8. Simplify:   4/8 = ______     9/12 = ______

Answers and marking guide

Answers

1. 7/9
2. 5/8
3. 7/10 (10/10 − 3/10)
4. 7/8 (4/8 + 3/8)
5. 1/6 (5/6 − 4/6)
6. 7/10 (6/10 + 1/10)
7. 6/8 + 1/8 = 7/8 of a kilometre.
8. 4/8 = 1/2; 9/12 = 3/4.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by making the parts match before adding or taking away.

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: adding and taking away parts of the same size, renaming to add and to take away, and strategies.