Unit Fractions and the Whole: a week of ready-to-teach maths

Five days of lessons for Year 3 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out fraction strips and 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 strips and the make-a-whole 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. The whole week rests on one idea: a unit fraction is one of a number of equal parts of one whole. The bottom number says how many equal parts the whole was cut into, and the top number counts how many of those parts you have. Same-size pieces add up, and the whole is back when the count reaches the bottom number.

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 makes the equal parts and names the unit fraction; Day 2 counts copies of it up to the whole; Day 3 puts the same fractions on a number line; Day 4 adds same-size pieces and meets a piece with two names; and Day 5 asks how much more makes a whole. It builds on Halves, Quarters, Eighths from Year 2, where children folded and shared, and it is the ground that every later fraction lesson stands on.

Materials for the week (one trip)

• From the classroom: scissors, pencils, coloured pencils, this pack printed.
• Paper strips for folding: cut a few A4 sheets into long strips, three per child.
• For Day 3: a strip of masking tape along the floor, with 0 at one end and 1 at the other.
• Cut out once, use all week: the fraction strips and the make-a-whole cards in this pack.

Words for the word wall

whole, equal parts, unit fraction, half, third, quarter, fifth, tenth, numerator, denominator, top number, bottom number, number line, the same amount

Dear families

This week in maths, Year 3 is learning about fractions of one whole: halves, thirds, quarters, fifths and tenths. We cut wholes into equal parts, count the parts, place fractions on a number line, and put pieces back together to make a whole.

Try this at home

• Share food fairly: cut toast, a sandwich or a pizza into equal parts and name them. Are the parts really equal?
• Count the pieces as they are eaten: one quarter gone, two quarters gone. How much is left?
• Fold a piece of paper into quarters, then tenths if you can. Which piece is bigger, a quarter or a tenth?
• Ask: if we have eaten 3/5 of the block, how much more would make the whole?

My fractions this week

Fill one row a day. Tick when you have checked the parts are equal.

Printed from the free seegongsik Unit Fractions and the Whole teaching pack · seegongsik.com/au/y3/number/AC9M3N02/pack

Equal parts make a unit fraction

A fraction begins with a fair cut. Children fold and cut wholes into equal parts and name one part. The bottom number says how many equal parts the whole was cut into.

We are learning to

• explain that a unit fraction is one of a number of equal parts of one whole,
• name and write halves, thirds, quarters, fifths and tenths (1/2, 1/3, 1/4, 1/5, 1/10),
• explain why 1/10 is smaller than 1/2 even though 10 is bigger than 2.

Success criteria

• I can show and name a unit fraction of a strip or shape.
• I can say which of two unit fractions is bigger, and why.

You need

Three paper strips per child for folding. The fraction strips (cut-out sheet 1), one set per pair. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after halves and quarters; start Session B with the thirds fold.

Watch for these ideas

• Calling three unequal pieces thirds. The parts must be the same size.
• Thinking 1/10 is bigger than 1/2 because 10 beats 2. More cuts make thinner pieces.
• Counting the cut lines instead of the parts: three lines inside a bar make four parts.

Answers

• Shade and name: 1/2, 1/3, 1/4, 1/5, 1/10. Bigger piece: 1/2, 1/3, 1/5.
• Are these quarters? A yes; B no (strips of different widths); C yes; D no (the cuts miss the centre).
• Biggest to smallest: 1/2, 1/3, 1/4, 1/5, 1/10.

Fair parts

Shade one part and name it

Each bar is one whole, cut into equal parts. Shade one part. Write the fraction it shows.

Which piece is bigger? Circle it.

1/2    or    1/10

1/3    or    1/4

1/5    or    1/10

Are these quarters?

Biggest piece to smallest

Put these in order, biggest piece first: 1/4, 1/2, 1/10, 1/3, 1/5

________, ________, ________, ________, ________

Count in unit fractions

Every fraction with the same bottom number is a count of the unit fraction: 3/4 is three copies of 1/4. The top number counts the pieces; the bottom number says how big each one is.

We are learning to

• count on in quarters, fifths, tenths and thirds and say when we reach one whole,
• read a fraction such as 3/4 as three copies of 1/4,
• write the fraction a shaded bar shows, and shade a bar to show a fraction.

Success criteria

• I can count in unit fractions up to one whole.
• I can say what the top and the bottom numbers mean.

You need

The fraction strips from Day 1, one set per pair. Coloured pencils. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after 3/4 and 2/5; start Session B with the fraction chant.

Watch for these ideas

• Swapping the numbers: 4/3 for three quarters. The bottom number is the size of the piece.
• Counting pieces of any size. Three pieces are three quarters only if each is a quarter.
• Not seeing 4/4 or 5/5 as one whole. When the count reaches the bottom number, the whole is back.

Answers

• Shaded: 2/5, 3/4, 7/10, 2/3. Shade it: 3 of 5 parts; 1 of 4 parts; 6 of 10 parts.
• Count on: 3/5, 4/5, 5/5; 8/10, 9/10, 10/10; 2/3, 3/3. Each ends on one whole.
• Gaps: 3 copies of 1/4; 7 copies of 1/10; 5 copies of 1/5 make one whole.

Copies of a unit fraction

What fraction is shaded?

Shade it

Count on to one whole

1/5, 2/5, ______, ______, ______ = 1 whole

6/10, 7/10, ______, ______, ______ = 1 whole

1/3, ______, ______ = 1 whole

Fill the gaps

3/4 is ______ copies of 1/4.

7/10 is ______ copies of ______.

______ copies of 1/5 make one whole.

Fractions on the number line

Fractions are positions too: they fill the gaps between 0 and 1. Cut the step from 0 to 1 into equal parts and every mark is a count of one unit fraction, and order is easy to see.

We are learning to

• cut a 0 to 1 number line into equal steps of fifths, quarters or tenths,
• label the marks as counts of a unit fraction (1/5, 2/5, 3/5 and so on),
• say which of two fractions with the same bottom number is further along, and so bigger.

Success criteria

• I can label the marks on a 0 to 1 line.
• I can mark a fraction on a line and say which of two is bigger.

You need

A two-metre strip of masking tape on the floor marked 0 and 1. A paper strip per child. The worksheet.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Writing 1/5 on the 0 mark. Zero is the start; 1/5 is the end of the first step.
• Counting marks instead of steps: a fifths line has six marks but five steps.
• Thinking fractions are not numbers. They are positions, and they can be ordered.

Answers

• Labels: 1/5 to 4/5; 1/4, 2/4, 3/4; 1/10 to 9/10. Marks: 3/5 on the third mark; 1/4 and 3/4 on the first and third; 7/10 on the seventh.
• Further along: 3/5, 3/4, 9/10.
• Steps: 10 steps of 1/10 reach 1. 3/4 is 3 steps of 1/4. 2/5 needs 3 more steps of 1/5.

Fractions have a place

Label the lines

Each line goes from 0 to 1 in equal steps. Write a fraction under every mark between 0 and 1.

Which is further along? Circle it.

3/5    or    2/5

1/4    or    3/4

6/10    or    9/10

How many steps?

From 0, how many steps of 1/10 reach 1? ______

3/4 is ______ steps of 1/4 from 0.

2/5 needs ______ more steps of 1/5 to reach 1.

Same-size pieces add up

Same-size pieces combine without fuss: 3/4 and 1/4 make 4/4, the whole again. The bottom number stays because the piece size has not changed. A finer cut can give a piece a second name.

We are learning to

• add fractions with the same bottom number by counting the pieces,
• say whether a sum makes one whole, and how much is missing if not,
• show that 1/2 and 2/4 (and 5/10) cover the same amount of a bar.

Success criteria

• I can add two fractions with the same bottom number and say if they make a whole.
• I can show with strips that 1/2 and 2/4 are the same amount.

You need

The fraction strips and the make-a-whole cards (cut-out sheet 2), one set each per pair. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after topping up bars; start Session B with the finer cut.

Watch for these ideas

• Adding the bottom numbers too: 2/5 + 3/5 = 5/10. The pieces are still fifths: 5/5, one whole.
• Thinking 2/4 is more than 1/2. Lay the strips side by side: the same length.
• Calling 9/10 a whole because it is nearly full. A whole needs all ten tenths.

Answers

• Sums: 4/4 = 1 (yes); 5/5 = 1 (yes); 9/10 (no); 3/3 = 1 (yes); 3/4 (no).
• Same amount: 1/2 = 2/4; 1/2 = 5/10; 1/5 = 2/10.
• Alex is not right: 2 fifths and 3 fifths make 5 fifths, one whole; 5/10 is only half.
• Make-a-whole pairs: 1/4, 3/4; 2/5, 3/5; 1/3, 2/3; 3/10, 7/10; 1/2, 1/2; 1/5, 4/5; 6/10, 4/10; 1/10, 9/10.

Pieces that add up

Add the pieces

Same amount, new name

The top bar shows the shaded fraction. Shade the same amount on the bar below it, then write its new name.

Explain it

Alex says 2/5 + 3/5 = 5/10. Is Alex right? Draw or write why.

How much more makes a whole?

How much more makes one whole? The empty parts answer it. Seeing the gap as a fraction is completing the whole read backwards, and it is how we know how much of a recipe or trip is left.

We are learning to

• find the fraction that completes one whole by counting the empty parts,
• solve everyday problems about how much is left or still to go,
• draw a bar to show and check our answer.

Success criteria

• I can find how much more makes one whole.
• I can draw a bar that proves my answer.

You need

The fraction strips and the make-a-whole cards. The worksheet, one per child. The unit’s self-check quiz.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Choosing the fraction already there (1/4) instead of what is missing.
• Choosing the whole (4/4). The question asks for the gap, not the full bar.
• Giving the part eaten when the story asks what is left. Read the question again.

Answers

• Missing piece: 3/5 + 2/5; 1/4 + 3/4; 6/10 + 4/10; 1/3 + 2/3. Make it whole: 3/10; 2/4; 1/5.
• Stories: 3/4 of the damper is left; 3/10 of the chocolate is left; 3/5 of the walk is still to go.
• Bars: cut into the right number of equal parts, with the eaten or walked parts marked.

The missing piece

How much more makes a whole?

Each bar is one whole. Write the fraction that is shaded and the fraction that is missing.

Make it whole

7/10 + ______ = 1     2/4 + ______ = 1     4/5 + ______ = 1

Story problems

Fraction strips

Cut along the dashed lines. Every row is the same length as the whole strip, so a piece laid on another shows which is bigger. Keep each row in its own envelope. One set per pair.

Teacher note: the tenths are narrow, so cut them last and slowly. Children can colour each row a different colour before cutting, which makes sorting quicker.

Make-a-whole cards

Cut out the sixteen cards. They make eight pairs, and every pair adds to exactly one whole. Play it as memory: cards face down, turn over two, keep the pair if it makes one whole.

Teacher note: the pairs are 1/4 and 3/4, 2/5 and 3/5, 1/3 and 2/3, 3/10 and 7/10, 1/2 and 1/2, 1/5 and 4/5, 6/10 and 4/10, 1/10 and 9/10. A child who claims a pair must say why it makes a whole.

What we know: Unit Fractions and the Whole

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

1. Shade one part of this bar. One part is called one ________ and written ____.
2. Which piece is bigger, 1/5 or 1/10? ______ How do you know? ______________________________
3. What fraction is shaded? ______
4. 4/5 is ______ copies of ______.
5. Mark 3/4 on the line with a dot.
6. 2/5 + 3/5 = ______ Is that one whole? ______
7. 1/2 = ____ /10
8. A pizza is cut into 3 equal slices. Two slices are eaten. What fraction is left? ______

Answers and marking guide

Answers

1. One part shaded; one third, written 1/3.
2. 1/5. The whole is cut into fewer parts, so each part is bigger.
3. 7/10.
4. 4 copies of 1/5.
5. The dot sits on the third mark after 0, one step before 1.
6. 5/5, and yes: five fifths make one whole.
7. 5 (1/2 = 5/10).
8. 1/3 (three thirds make the whole pizza, and two are eaten).

A quick three-level guide

Eight questions, three ideas. A child at standard answers most questions and can explain with a bar or a line, not just the digits.

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: equal parts, counting in unit fractions, the number line, adding pieces, and the missing piece.