Comparing 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 fraction 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 fraction 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 are easy to compare once they are counted in parts of the same size. With the same denominator, the larger numerator wins. When one denominator is a multiple of the other, rename one fraction by multiplying its top and bottom by the same number: 2/3 becomes 4/6 and sits beside 5/6. A bigger denominator means smaller parts, so 3/4 is larger than 5/8.

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.

How we write fractions

This pack prints fractions with a slash, 3/4, so they print cleanly; children write them with a line between top and bottom. A mixed numeral such as 1 1/4 is one and a quarter: one whole and a quarter more. The denominators stay related, halves with quarters and eighths, thirds with sixths, ninths and twelfths, as the curriculum asks for in Year 5.

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 finds fractions that name the same amount; Day 2 compares fractions cut into the same parts; Day 3 gives every fraction a place on the number line; Day 4 renames one fraction so two can be compared; and Day 5 orders whole sets, mixed numerals too. It builds on the Year 4 equivalent fractions and on this year’s factors and multiples, and it is the ground for adding and subtracting fractions with related denominators next.

Materials for the week (one trip)

• From the classroom: scissors, rulers, coloured pencils, envelopes for the cards, this pack printed.
• For Day 2: two strips of paper the same length per child, to fold (optional).
• Cut out once, use all week: the fraction wall and the 16 fraction cards in this pack. No maths equipment to buy.

Words for the word wall

fraction, numerator, denominator, equivalent, unit fraction, related denominators, common denominator, multiple, mixed numeral, number line, compare, order

Dear families

This week in maths, Year 5 compares and orders fractions. We find fractions that name the same amount, such as 1/2 = 2/4 = 4/8; compare fractions with the same denominator (5/8 is more than 3/8); rename one fraction to compare others (2/3 is 4/6, so it is less than 5/6); and place fractions and mixed numerals on a number line.

Try this at home

• Fold a sheet of paper into halves, then quarters, then eighths. How many eighths make one half?
• With measuring cups, ask which holds more, the 1/2 cup or the 1/3 cup, and why.
• Ask which is more: 3/4 of a pizza or 5/8 of the same pizza.
• Put the amounts in a recipe in order, smallest first: 1/4 cup, 3/4 cup, 1/2 cup.

My fractions this week

Fill one row a day. Compare two fractions you find or make at home.

Printed from the free seegongsik Comparing Fractions teaching pack · seegongsik.com/au/y5/number/AC9M5N03/pack

Same amount, different names

Children use the fraction wall to find fractions that name the same amount, such as 1/2, 2/4 and 4/8, and find the pattern: multiply the top and the bottom by the same number. Equivalent fractions are the tool for every comparison this week.

We are learning to

• find equivalent fractions on the fraction wall,
• make an equivalent fraction by multiplying the numerator and the denominator by the same number,
• explain why adding the same number to the top and the bottom changes the amount.

Success criteria

• I can write three fractions equal to 1/2 and two equal to 2/3.
• I can find the missing number in 3/4 = ?/12.

You need

The fraction wall (cut-out sheet 1), one per pair, cut into its eight strips. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by lining up 2/3 and 4/6 on the wall.

Watch for these ideas

• Adding the same number to the top and the bottom (2/3 to 3/4). The amount changes; multiply instead.
• Thinking 4/8 is more than 1/2 because the numbers are bigger. It is the same amount in smaller parts.
• Multiplying only the bottom (1/2 to 1/4). Top and bottom are multiplied by the same number.

Answers

• Part A: 4/6 and 8/12; 6/8. Part B: 1/2 = 2/4 = 3/6 = 4/8 = 5/10; 2/3 = 4/6 = 6/9 = 8/12; 3/4 = 6/8 = 9/12; 5/6 = 10/12.
• Part C: yes, no, no, yes, yes, no. Part D: adding 1 to the top and the bottom changes the amount (3/4 is more than 2/3); multiplying top and bottom by 2 gives 4/6, which is equal to 2/3.

Same amount, different names

A. Shade the same amount on each bar, then write the fraction

B. Fill in the missing numbers

1/2 = ____/4 = ____/6 = ____/8 = ____/10

2/3 = ____/6 = ____/9 = ____/12

3/4 = ____/8 = ____/12

5/6 = ____/12

C. Do they name the same amount? Circle yes or no.

2/4 and 1/2   yes / no2/3 and 3/4   yes / no1/3 and 2/9   yes / no4/8 and 3/6   yes / no6/8 and 3/4   yes / no2/6 and 1/4   yes / no

D. Ben’s idea

Ben says 2/3 = 3/4, because he added 1 to the top and 1 to the bottom. Is he right? How do you know?

___________________________________________________________

Same parts, compare the tops

Children compare fractions cut into parts of the same size: with the same denominator, the larger numerator is the larger fraction. Then they turn it round: with the same numerator, a larger denominator means smaller parts, so 1/3 is larger than 1/5.

We are learning to

• compare fractions with the same denominator by their numerators,
• order a set of fractions with the same denominator,
• compare fractions with the same numerator by the size of their parts.

Success criteria

• I can circle the larger of 5/12 and 7/12 and say why.
• I can explain why 1/3 is larger than 1/5.

You need

The fraction wall strips. Two paper strips of the same length per child, to fold (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B by folding the two strips.

Watch for these ideas

• Thinking 1/5 is bigger than 1/3 because 5 is bigger than 3. More parts in the whole means smaller parts.
• Looking at the denominators when they are the same. When the bottoms match, the tops decide.
• Ordering by one number only. Look at the top and the bottom every time.

Answers

• Part A: 7/12, 4/9, 6/7, 4/5. Part B: 1/8, 3/8, 5/8, 7/8; 1/10, 3/10, 7/10, 9/10.
• Part C: 1/3, 2/5, 1/6, 3/4. Part D: one third is larger; the whole is cut into only three parts, so each part is bigger than a fifth, where the same whole is cut into five.

Same parts, compare the tops

A. Same denominator: circle the larger fraction

5/12    7/124/9    2/96/7    5/73/5    4/5

B. Put them in order, smallest first

C. Same numerator: circle the larger fraction

1/3    1/52/9    2/51/12    1/63/4    3/8

D. One third or one fifth?

Which is larger, 1/3 or 1/5? Draw two strips the same length to show it, then explain.

___________________________________________________________

A place on the line

Children give fractions a place on the number line: they cut the line from 0 to 1 into equal steps, label the marks and mark fractions with arrows. Equivalent fractions land on the same point, and mixed numerals sit past 1.

We are learning to

• label a number line cut into quarters, sixths or eighths,
• mark a fraction by counting steps from 0, renaming it first when needed (2/3 is 4 sixths),
• place mixed numerals between 1 and 2.

Success criteria

• I can mark 2/3 on a line cut into sixths.
• I can write the number at an arrow on a line from 0 to 2.

You need

The fraction wall strips, to lay along a line. A masking-tape line on the floor marked 0, 1 and 2 (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by marking 2/3 together.

Watch for these ideas

• Counting the marks instead of the steps, so 1/4 lands on the second mark. Count the jumps from 0.
• Putting 2/3 on the second mark of a sixths line. Rename it first: 2/3 = 4/6.
• Placing 1 1/4 between 0 and 1. The whole number says which whole it is in.

Answers

• Part A: 1/4, 2/4 (or 1/2), 3/4; 1/6, 2/6 (or 1/3), 3/6 (or 1/2), 4/6 (or 2/3), 5/6. Part B: 2/3 on step 4 of 6, 5/6 on step 5 of 6; 3/8 on step 3 of 8, 3/4 on step 6 of 8.
• Part C: A = 1 1/4; B = 3/4; C = 1 3/4; D = 2/4 (or 1/2); in order 2/4 (or 1/2), 3/4, 1 1/4, 1 3/4. Part D: 2/4, 3/6, 4/8.

A place on the line

A. Write the fraction under each mark

B. Mark each fraction with an arrow

C. Write the number at each arrow, then order them

A = ________B = ________C = ________D = ________

Smallest first: ________, ________, ________, ________

D. Same point

On a line from 0 to 1, which of these land on the same point as 1/2? Circle them.    2/4,   2/3,   3/6,   4/8,   5/8

Rename, then compare

Children compare fractions whose denominators are related, such as thirds and sixths: they rename one fraction so both share a denominator, then compare the numerators. The fraction with the bigger denominator is not always bigger: 3/4 is larger than 5/8.

We are learning to

• spot related denominators, where one is a multiple of the other,
• rename one fraction so both share the larger denominator,
• compare and explain, including in story problems.

Success criteria

• I can rename 2/3 in sixths to compare it with 5/6.
• I can say who ate more pizza and prove it with one denominator.

You need

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

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 3/8 and 1/2 on the board.

Watch for these ideas

• Thinking the fraction with the bigger denominator is bigger (5/8 more than 3/4). Rename: 3/4 = 6/8.
• Renaming only the bottom (2/3 to 2/6). The top is multiplied too: 4/6.
• Multiplying by the wrong number. Find what turns the small denominator into the large one (3 × 2 = 6), then use it on the top.

Answers

• Part A: 4/10 and 3/10, so 2/5; 5/6 and 4/6, so 5/6; 4/8 and 7/8, so 7/8; 7/12 and 9/12, so 3/4; 4/9 and 3/9, so 4/9. Part B: 1/2 = 4/8; 2/3 > 7/12; 3/10 < 2/5; 5/6 = 10/12; 3/4 > 5/8.
• Part C: Mia (3/8 and 2/8); the second jug (4/6 and 5/6); Ava (7/10 and 6/10). Part D: 5/6, because it is 2/12 short of 1 and 7/12 is 5/12 short.

Rename, then compare

A. Rename so both have the same denominator, then circle the larger

B. Write <, > or =

1/2 ____ 4/82/3 ____ 7/123/10 ____ 2/55/6 ____ 10/123/4 ____ 5/8

C. Fraction stories

D. Closer to one whole

Which is closer to 1, 5/6 or 7/12? ________   How much short of 1 is each one? ________   ________

In order, smallest first

Children order sets of fractions and mixed numerals: rename to one denominator and order by the numerators, and order mixed numerals by the whole number first. A number line checks every order. The week ends with the unit quiz as a class game.

We are learning to

• order fractions with related denominators by renaming them to one denominator,
• order mixed numerals by the whole number first, then the fraction,
• check an order on a number line.

Success criteria

• I can order 3/4, 5/8, 1/2 and 7/8, smallest first.
• I can explain why 1 1/4 is larger than 3/4.

You need

The fraction cards (cut-out sheet 2), one set per group of four. The worksheet, one per child. The interactive unit open for the quiz game.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Ordering by the denominators, so 1/2, 1/4, 1/8 looks smallest first. A bigger denominator means smaller parts.
• Ordering mixed numerals by the fraction part only, so 1 1/4 comes before 3/4. The whole number decides first.
• Comparing numerators before renaming, so 5/8 goes after 3/4 because 5 is more than 3.

Answers

• Cards: halves, quarters and eighths: 1/4,   3/8,   1/2,   5/8,   3/4,   7/8,   1 1/4,   1 1/2; thirds, sixths and twelfths: 1/6,   1/3,   5/12,   2/3,   5/6,   11/12,   1 1/6,   1 1/3.
• Part A: 1/2,   5/8,   3/4,   7/8; 1/3,   1/2,   2/3,   5/6. Part B: 1/2,   3/4,   1 1/4,   1 1/2,   2; 1 2/3,   1 5/6,   2 1/6,   2 1/3. Part C: Jo should have 1/8,   1/4,   1/2; 1 1/4 is larger than 3/4, because it is more than one whole.

In order, smallest first

A. Rename, then order, smallest first

B. With mixed numerals

C. Spot the slip

Jo ordered 1/2,   1/4,   1/8 this way, smallest first, because 2 is the smallest denominator. What is the right order?

______________________________________________

Kai says 1 1/4 is smaller than 3/4, because 1/4 is smaller than 3/4. What would you tell Kai?

___________________________________________________________

The fraction wall

Each strip is one whole, the same length. Cut the strips apart, one per pair, and keep them whole to lay side by side; cut a strip into its pieces only when a lesson asks. Pieces that line up exactly name the same amount: two quarters line up with one half.

Teacher note: the eight strips hold every denominator this week uses. Quarters and eighths line up with the halves; sixths, ninths and twelfths line up with the thirds. Two denominators are related when one is a multiple of the other, such as 3 and 6, 4 and 8, or 6 and 12.

Fraction cards

Cut out the sixteen cards, one set per group. Each card names its family under the fraction. Order each family, smallest first, then check the order on the fraction wall (Day 5).

Teacher note: the order for each family is in the answers on the Day 5 plan.

What we know: Comparing Fractions

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

1. Write two fractions equivalent to 2/3.   __________   __________
2. Fill the gap: 3/4 = ______/12
3. Circle the larger:   5/9    7/9
4. Circle the larger:   1/4    1/6
5. Write <, > or = : 3/5 ____ 7/105/8 ____ 1/24/6 ____ 2/3
6. What fraction is at each arrow?   A = ________   B = ________
7. Put these in order, smallest first: 2/3, 1/6, 1/2, 5/6.   ______________________________
8. Put these in order, smallest first: 1 1/3, 5/6, 1 1/6, 2/3.   ______________________________

Answers and marking guide

Answers

1. Any two of 4/6, 6/9, 8/12 (or others made by multiplying top and bottom by the same number).
2. 9 (3/4 = 9/12).
3. 7/9 (same denominator, larger numerator).
4. 1/4 (same numerator, bigger parts).
5. 3/5 < 7/10; 5/8 > 1/2; 4/6 = 2/3.
6. A = 3/8; B = 6/8 (6/8 is also 3/4).
7. 1/6, 1/2, 2/3, 5/6.
8. 2/3, 5/6, 1 1/6, 1 1/3.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by renaming to one denominator or by the size of the parts.

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: equivalent fractions, the same denominator, the number line, related denominators and ordering.