Equivalent Fractions: 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 fraction-wall strips and matching 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 strips and 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 short: equivalent fractions shade the same amount of the same whole. Cut every half into two and one half becomes two quarters; the amount has not changed, only the number of pieces. That is why multiplying the top and the bottom by the same number makes an equivalent fraction.

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 writes fractions with a slash, 3/4, as the unit on screen does. When you write on the board, the stacked form with the line across is just as good. Read 3/4 as “three quarters” and 3/10 as “three tenths”, so the size of the part is in the name.

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 gives every fraction a size on a bar; Day 2 lines bars up to find equal amounts; Day 3 turns what the wall shows into a rule (multiply top and bottom by the same number); Day 4 connects fractions to the decimals from Tenths and Hundredths; and Day 5 tests and sorts equivalents. It builds on the unit fractions of Year 3, and comparing, adding and simplifying fractions in later years all rest on it.

Materials for the week (one trip)

• From the classroom: scissors, glue or a paper clip per child, pencils, coloured pencils, this pack printed.
• Paper strips for folding on Day 1, all the same length (scrap A4 cut into long strips is fine).
• Cut out once, use all week: the fraction-wall strips and the fraction and decimal cards in this pack. No maths equipment to buy.

Words for the word wall

fraction, whole, equal parts, numerator, denominator, equivalent, fraction wall, half, quarter, eighth, third, sixth, fifth, tenth, hundredth, decimal

Dear families

This week in maths, Year 4 explores equivalent fractions: different fractions that name the same amount, such as one half and two quarters. We find them on a fraction wall, make them by multiplying, and connect fractions to decimals such as 0.5 and 0.25.

Try this at home

• Cut a sandwich in half, then cut each half again. Two quarters cover the same as one half.
• Fold a sheet of paper into 2, then 4, then 8 equal parts. Shade half and count how many eighths that is.
• Look at a measuring jug or a ruler for halves and quarters, and at prices for 0.50 and 0.25.
• Ask which is more, 3/4 of a pizza or 6/8 of the same pizza.

My fractions this week

Fill one row a day. Find a fraction at home and write an equivalent for it.

Printed from the free seegongsik Equivalent Fractions teaching pack · seegongsik.com/au/y4/number/AC9M4N03/pack

A fraction as a bar

Children give every fraction a size on a bar. The bottom number says how many equal parts the whole is cut into; the top number says how many of those parts are taken. They read and shade fractions beyond unit fractions, such as 3/4 and 5/8, and compare them with a half.

We are learning to

• explain what the top and bottom numbers of a fraction tell us,
• read and shade fractions such as 3/4, 2/3 and 5/8 on a bar,
• decide whether a fraction is more than, less than or exactly a half.

Success criteria

• I can write the fraction a bar shows and shade a fraction on a bar.
• I can say if a fraction is more or less than a half, and why.

You need

Paper strips of the same length, two per child. The fraction-wall strips (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 by shading 2/5 together.

Watch for these ideas

• Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4. More parts means smaller parts.
• Counting the unshaded parts as the top number. The top number counts the parts taken.
• Parts that are not equal. Each part of the bar must be the same size.

Answers

• Part A: 3/4, 2/3, 5/8, 3/10. Part B: shade 2 of the 5 parts and 4 of the 6 parts.
• Part C: 3/8 is less than half; 5/6 is more than half; 2/4 is exactly half; 1/3 is less than half. Part D: 4 quarters; 8 eighths; 10 tenths.

Fractions on a bar

Every bar is the same whole. The bottom number cuts it into equal parts; the top number counts the parts taken.

A. What fraction is shaded?

B. Shade the fraction

C. More than half, less than half, or exactly half? Circle one.

3/8:   more  /  less  /  exactly half

5/6:   more  /  less  /  exactly half

2/4:   more  /  less  /  exactly half

1/3:   more  /  less  /  exactly half

D. How many make one whole?

____ quarters make one whole.    ____ eighths make one whole.    ____ tenths make one whole.

Same amount, different names

Children line up fraction-wall strips of the same length and find pieces that cover the same amount. One half, two quarters and four eighths cover the same length: they are equivalent fractions, one amount with different names.

We are learning to

• explain that equivalent fractions cover the same amount of the same whole,
• use a fraction wall to find equivalents for halves, quarters, thirds and fifths,
• notice that equivalents come in related families: halves, quarters and eighths; thirds and sixths; fifths and tenths.

Success criteria

• I can use the fraction wall to find an equivalent fraction.
• I can explain why 1/2 and 2/4 name the same amount.

You need

The fraction-wall strips (cut-out sheet 1), cut into rows, 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 by building the thirds and sixths.

Watch for these ideas

• Thinking 2/4 is more than 1/2 because there are more pieces. The pieces are smaller.
• Thinking two fractions with the same top number are equal (3/4 and 3/8).
• Using strips of different lengths. Equivalence only works on the same whole.

Answers

• Part A: 1/2 = 2/4; 1/2 = 4/8; 3/4 = 6/8; 1/4 = 2/8. Part B: 1/3 = 2/6; 2/3 = 4/6; 1/5 = 2/10; 4/5 = 8/10.
• Part C: 2/4 = 1/2 true; 1/3 = 2/6 true; 3/4 = 3/8 false; 4/8 = 2/4 true; 2/5 = 4/10 true; 1/2 = 3/5 false.

The fraction wall

Every row is the same whole. Look straight down the wall to find pieces that cover the same amount.

A. Halves, quarters and eighths

1/2 = ____/41/2 = ____/83/4 = ____/81/4 = ____/8

B. Thirds and sixths, fifths and tenths

1/3 = ____/62/3 = ____/61/5 = ____/104/5 = ____/10

C. True or false? Check on the wall, then circle.

2/4 = 1/2   true / false1/3 = 2/6   true / false3/4 = 3/8   true / false4/8 = 2/4   true / false2/5 = 4/10   true / false1/2 = 3/5   true / false

Making equivalents

Children turn what the wall showed into a rule: multiply the top and the bottom by the same number and the fraction keeps its size. Cutting every part into two doubles the number of parts and the number shaded, so 1/2 becomes 2/4. The new bottom number is a related denominator.

We are learning to

• make an equivalent fraction by multiplying the top and bottom by the same number,
• explain with a bar why this keeps the amount the same,
• find a missing number to make two fractions equivalent (1/3 = ?/6).

Success criteria

• I can make an equivalent fraction with a related denominator.
• I can find the missing number in a pair of equivalent fractions.

You need

The fraction-wall strips from Day 2, one set per pair, to check answers. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 1/3 = ?/6.

Watch for these ideas

• Adding instead of multiplying: 1/2 to 2/3 by adding 1 to both. On a bar, 2/3 is more than a half.
• Multiplying only the bottom: 1/3 to 1/6. That makes the parts smaller but takes the same number, so the amount shrinks.
• Thinking a bigger denominator means a bigger fraction. 4/8 has bigger numbers than 1/2 but the same size.

Answers

• Part A: 1/2 = 3/6; 1/4 = 2/8; 2/5 = 4/10; 3/4 = 9/12.
• Part B: 2, 6, 10, 6, 12. Part C: any of 2/8, 3/12, 4/16, 5/20, 25/100 (top times k, bottom times k).

Multiply top and bottom

Multiply the top and the bottom by the same number. The fraction gets more, smaller parts, but the amount stays the same.

A. Make the equivalent

Check on the bar: draw dashed lines to cut every part into as many smaller parts as the number you multiply by.

B. Find the missing number

1/3 = ____/63/5 = ____/101/2 = 5/____3/4 = ____/82/3 = 8/____

C. A family for 1/4

Write as many fractions equivalent to 1/4 as you can.

Fractions and decimals

Children connect fractions to the decimals from Tenths and Hundredths. A fraction with a bottom number of 10 or 100 is already a decimal: 3/10 is 0.3, 9/100 is 0.09. Other fractions are first rewritten as tenths or hundredths: 1/2 = 5/10 = 0.5 and 1/4 = 25/100 = 0.25.

We are learning to

• write tenths and hundredths as decimals, and decimals as fractions,
• use equivalent fractions to write 1/2, 1/4, 3/4 and 1/5 as decimals,
• explain that a fraction and its decimal name the same amount.

Success criteria

• I can write a fraction with 10 or 100 on the bottom as a decimal.
• I can show that 1/2 = 0.5 and 1/4 = 0.25 using equivalent fractions.

You need

The tenths strip from the fraction wall. A hundred-square from Tenths and Hundredths if you have one (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 1/2 = 5/10 = 0.5.

Watch for these ideas

• Writing a fraction’s digits after the point: 1/4 as 0.14 or 3/4 as 0.34. The decimal is the amount, not the digits.
• Writing 9/100 as 0.9. Nine hundredths has a zero in the tenths: 0.09.
• Thinking 1/5 is 0.5 because of the 5. One fifth is two tenths: 0.2.

Answers

• Part A: 3/10 = 0.3; 7/10 = 0.7; 5/10 = 0.5 (5/10 is also 1/2). Part B: 1/4 = 25/100 = 0.25; 3/4 = 75/100 = 0.75; 9/100 = 9/100 = 0.09; 1/5 = 20/100 = 0.2.
• Part C: 1/2 = 0.5; 1/10 = 0.1; 3/4 = 0.75. Part D: 4/10; 7/100; 5/10 or 1/2; 25/100 or 1/4.

Fractions and decimals

A. Shade the tenths and write the decimal

B. Write it in hundredths, then as a decimal

C. Circle the decimal that matches

1/2:   0.2     0.5     0.12

1/10:   0.01     1.0     0.1

3/4:   0.75     0.34     0.7

D. Write each decimal as a fraction

0.4 = ____/10    0.07 = ____/100    0.5 = ____/10 = 1/____    0.25 = ____/100 = 1/____

Spot the equivalent

Children test whether two fractions are equivalent by scaling one to the other or by picturing both on the same whole, then gather the week into a table of fractions, their equivalents and their decimals.

We are learning to

• test whether two fractions are equivalent by finding the number that scales one to the other,
• spot an equivalent among fractions that look alike but are not (1/4 and 4/2),
• list an equivalent and a decimal for common fractions.

Success criteria

• I can pick the equivalent fraction and explain how I know.
• I can fill a row of the table: fraction, equivalent, decimal.

You need

The fraction and decimal cards (cut-out sheet 2), one set per group of four. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Choosing a fraction with the same digits turned round (1/4 and 4/2). 4/2 is two wholes.
• Expecting every fraction to have a short decimal. 1/3 has no tenths or hundredths form yet.
• Testing with one number only: 3/5 and 3/10 share a top number but not an amount.

Answers

• Part A: 1/4 = 2/8; 3/5 = 6/10; 2/4 = 1/2; 1/3 = 3/9.
• Part B: 1/2, 2/4, 0.5; 1/4, 2/8, 0.25; 3/4, 6/8, 0.75; 1/10, 10/100, 0.1; 2/5, 4/10, 0.4; 1/3, 2/6, no short decimal (any correct equivalent counts). Part C: any three pairs that name the same amount.

Spot the equivalent

A. Circle the fraction equivalent to the first one

1/44/2       2/8       1/8

3/53/10       5/3       6/10

2/41/2       2/8       4/2

1/31/6       3/9       3/1

Next to each row, write how you know: the number that scales one fraction to the other.

B. Fractions, equivalents and decimals

C. Match-up game: three pairs I found

__________ = __________    __________ = __________    __________ = __________

Fraction-wall strips

Cut along the outside of each row to make eight strips, all the same length. Keep them whole to build the wall (Day 2); cut single parts off a spare copy when you need pieces. One set per pair.

Teacher note: the rows are the whole, halves, thirds, quarters, fifths, sixths, eighths and tenths. Every strip is exactly the same length, so equal amounts line up when the strips are stacked, the same picture as “Equivalent fractions” on screen.

Fraction and decimal cards

Cut out the 24 cards for the match-up game (Day 5). Turn them face down, flip two at a time, and keep the pair if both cards name the same amount. Each card has three partners.

Match-up cards

Teacher note: the families are 1/2, 2/4, 5/10, 0.5; 1/4, 2/8, 25/100, 0.25; 3/4, 6/8, 75/100, 0.75; 1/5, 2/10, 20/100, 0.2; 1/10, 10/100, 0.1, 0.10; and 1/3, 2/6, 3/9, 4/12. The thirds have no decimal card on purpose: ask why.

What we know: Equivalent Fractions

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

1. What fraction is shaded? ________
2. Fill the gaps: 1/2 = ____/4 = ____/8
3. Make an equivalent: 2/5 = ____/10    1/3 = 4/____
4. Circle the fraction equivalent to 3/4:   3/8    6/8    4/3
5. Write as a decimal: 7/10 = ______    1/2 = ______    25/100 = ______
6. Write as a fraction: 0.3 = ____/10    0.75 = ____/100 = 3/____
7. Are 2/3 and 4/6 equivalent? Show how you know. ______________________________
8. Mia ate 2/8 of a pizza and Sam ate 1/4 of the same-size pizza. Who ate more? ______ Why? ________________

Answers and marking guide

Answers

1. 5/8 (8 equal parts, 5 shaded).
2. 1/2 = 2/4 = 4/8.
3. 2/5 = 4/10 (times 2); 1/3 = 4/12 (times 4).
4. 6/8 (3/4 times 2 on top and bottom); 3/8 is less, and 4/3 is more than one whole.
5. 0.7; 0.5; 0.25.
6. 0.3 = 3/10; 0.75 = 75/100 = 3/4.
7. Yes: 2/3 times 2 on top and bottom is 4/6, or both shade the same amount of the same bar.
8. They ate the same amount: 2/8 = 1/4.

A quick three-level guide

Eight questions, three ideas. A child at standard answers most questions and can show an equivalence on a bar or by multiplying top and bottom by the same number.

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: bars, the wall, multiplying, decimals and spotting equivalents.