Halves, quarters and eighths: a week of ready-to-teach maths

Five days of lessons for Year 2 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out fraction tiles 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 two card sheets once; the tiles, 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 when.
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 model answers, so you can walk in and teach it.

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 lesson can also split into a short warm-up and a main session if your timetable runs small blocks.

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 one fair cut into two equal parts; Day 2 halves each half into quarters; Day 3 folds to eighths and sees the whole halving chain; Day 4 names the pieces and compares their sizes; and Day 5 asks half of what, so a half of a big whole and a half of a small whole are both halves and different amounts. It builds on fair sharing between two from Year 1, and it opens the way to fractions of shapes, objects and events in Measurement.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• From home or the craft box: a few long paper strips (cut printer paper the long way), a couple of round paper plates or paper circles, and a piece of fruit or some playdough for a real fair share.
• Cut out once, use all week: the fraction tiles, the fold-and-cut strips and the equal-or-not sorting cards in this pack. No maths equipment to buy.

Dear families

This week in maths, Year 2 learns about halves, quarters and eighths. We cut and fold wholes into equal parts, and we see how halving again and again makes the family: a half, then a quarter, then an eighth.

Try this at home

• Share something fairly between two: a sandwich, an apple, a piece of toast. Ask, are the two parts equal? Only then is it halves.
• Fold a piece of paper in half, and half again, and half again. Open it and count the equal parts.
• At dinner, cut a pancake or a pizza into quarters, then eighths. Ask which single piece is bigger, a quarter or an eighth.
• Ask half of what: half of a big glass of milk and half of a small glass are both halves, but not the same amount.

My fractions this week

Fill one row a day. Tick each way you cut or folded your whole into equal parts.

Printed from the free seegongsik Halves, Quarters, Eighths teaching pack · seegongsik.com/au/y2/number/AC9M2N03/pack

Two equal parts

Children meet the first law of fractions: a half is one of 2 equal parts of a whole. Two pieces are only halves when they are equal. Hands and paper convince faster than symbols, so fold and cut before you name.

We are learning to

• fold or cut a whole into 2 equal parts,
• explain that a half is one of 2 equal parts of a whole,
• tell halves from two pieces that are not equal.

Success criteria

• I can fold a shape into two equal parts.
• I can say why a big piece and a small piece are not halves.

You need

The equal-or-not sorting cards and a few fold-and-cut strips (cut-out sheet 2). Scissors and spare paper shapes to fold. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the sort. Start Session B by folding a new shape into halves, then the bigger-half challenge.

Watch for these ideas

• The bigger half: children and adults say it, but a half cannot be bigger or smaller. Halves are equal.
• Calling any 2 pieces halves: two pieces are only halves when they are equal.
• Judging by shape, not size: two equal parts can look different (a square cut corner to corner) and still be halves.

Answers

• Sorting cards, equal parts (halves): cards 1, 3, 5 and 7. Not equal: cards 2, 4, 6 and 8.
• Draw the fair cut: any line that makes two equal parts. A rectangle can be halved down the middle either way, a circle by any line through its centre, a square down the middle or corner to corner.
• Halves or not: yes, no, yes, no.
• Finish the sentence: equal (the same size). A half is one of 2 equal parts of a whole.

Halves must be equal

A half is one of 2 equal parts of a whole. Only equal parts are halves.

1. Draw the fair cut

Draw the whole, then draw one line that cuts it into two equal parts (halves).

2. Halves or not halves?

Read each cut. Write yes if the two parts are halves, or no if they are not.

3. Finish the sentence

Two pieces are halves only when they are ______________.

Halve again: quarters

Quarters are not a new idea; they are halves done twice. Halve a whole to make halves, then halve each half to make quarters. Four equal parts now fill the whole, and a quarter is half of a half.

We are learning to

• halve each half to make quarters,
• show that 4 equal parts fill one whole,
• explain that a quarter is half of a half.

Success criteria

• I can fold or cut a whole into 4 equal parts.
• I can say a quarter is half of a half.

You need

The fraction tiles (cut-out sheet 1). Paper strips or squares to fold twice. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the second fold. Start Session B with the tiles and the worksheet.

Watch for these ideas

• Treating a quarter as a brand-new idea, instead of half of a half.
• Making 4 pieces that are not equal and still calling them quarters; quarters must be equal.
• Losing count of how many quarters fill a whole (4) or a half (2).

Answers

• Fill the family: 2 halves; 2 quarters; 4 equal parts; half. A quarter is half of a half.
• Colour one-quarter: any 1 of the 4 equal parts; 3 more quarters finish the whole, so 4 quarters make the whole bar.
• Colour two-quarters: any 2 of the 4 parts; two-quarters is the same as one-half.

Halve the half

Fold and halve. Then halve again. Count the equal parts.

1. Draw the folds

Draw a whole. Draw one line to make halves. Draw two more lines to make quarters.

2. Fill in the family

1. 1 whole becomes ____ halves.
2. 1 half, halved, becomes 2 ______________.
3. A whole cut into quarters has ____ equal parts.
4. A quarter is half of a ____________.

3. Colour one-quarter

This bar has 4 equal parts. Colour one-quarter of it.

How many quarters make the whole bar? ____

4. Colour two-quarters

Colour two-quarters of this bar. Two-quarters is the same as one ____________.

Halve again: eighths

One more halving. Fold a strip in half three times and open it: eight equal parts, drawn by the creases with no ruler in sight. This is the halving chain, 1 whole, 2 halves, 4 quarters, 8 eighths, and an eighth is half of a quarter.

We are learning to

• fold a strip in half three times to make eighths,
• say the halving chain: 1, 2, 4 and 8 equal parts,
• explain that an eighth is half of a quarter.

Success criteria

• I can fold a strip into 8 equal parts.
• I can say how many eighths make a half and a quarter.

You need

The fold-and-cut strips (cut-out sheet 2) and the fraction tiles (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the three folds. Start Session B by matching the tiles and filling the worksheet.

Watch for these ideas

• Thinking you need a ruler to make eighths; three fair folds do it.
• Miscounting: three folds make 8 equal parts, not 3 or 6.
• Forgetting the links inside the whole: one-half is 4 eighths, one-quarter is 2 eighths.

Answers

• Count the folds: one fold makes 2 (halves); two folds make 4 (quarters); three folds make 8 (eighths).
• Colour one-eighth: any 1 of the 8 equal parts.
• Colour one-half: any 4 of the 8 parts; one-half is the same as 4 eighths.
• Colour one-quarter: any 2 of the 8 parts; one-quarter is the same as 2 eighths.

Fold to eighths

Fold a paper strip in half, then in half again, then in half once more. Open it and count.

1. Count the folds

1. One fold makes ____ equal parts. We call them halves.
2. Two folds make ____ equal parts. We call them quarters.
3. Three folds make ____ equal parts. We call them eighths.

2. Colour one-eighth

This strip has 8 equal parts. Colour one-eighth of it.

3. Colour one-half

Colour one-half of this strip. One-half is the same as ____ eighths.

4. Colour one-quarter

Colour one-quarter of this strip. One-quarter is the same as ____ eighths.

Name them and compare

Now name the pieces and compare their sizes. Here is the great fraction trap: eight sounds bigger than four, so an eighth must beat a quarter. The whole says no. The number names how many equal parts there are, and more parts make each part smaller.

We are learning to

• name halves, quarters and eighths of one whole,
• compare the sizes of one-half, one-quarter and one-eighth,
• explain that more equal parts make each part smaller.

Success criteria

• I can put one-half, one-quarter and one-eighth in size order.
• I can explain why one-half is bigger than one-quarter of the same whole.

You need

The fraction tiles (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after ordering the three tiles. Start Session B with the worksheet.

Watch for these ideas

• The big trap: thinking one-eighth is bigger than one-quarter because 8 is more than 4.
• Comparing pieces from different wholes; the comparison only holds for the same whole.
• Reading the name for size: eight tells you how many parts there are, not how big each one is.

Answers

• Name the pieces: Bar A has 2 equal parts, each is one-half; Bar B has 4, each is one-quarter; Bar C has 8, each is one-eighth.
• Circle the bigger piece: one-half; one-quarter; one-half.
• Order, biggest first: one-half, one-quarter, one-eighth.
• Finish the sentence: how many; how big.

Which piece is bigger?

Same whole every time. The more pieces you cut it into, the smaller each piece.

1. Name the pieces

Bar A

Bar A has ____ equal parts. Each piece is called one-____________.

Bar B

Bar B has ____ equal parts. Each piece is called one-____________.

Bar C

Bar C has ____ equal parts. Each piece is called one-____________.

2. Circle the bigger piece (same whole)

1. one-half    or    one-quarter
2. one-quarter    or    one-eighth
3. one-half    or    one-eighth

3. Put them in order

Write these from biggest to smallest: one-eighth, one-half, one-quarter.

4. Finish the sentence

In one-eighth, the 8 tells you how ____________ equal parts there are, not how ____________ each piece is.

Half of what?

A half is always half of something. Half of a big whole and half of a small whole are both honest halves and plainly different amounts. That is the point: a fraction names a part of its own whole. Today we share fairly and always ask, half of what?

We are learning to

• share a whole fairly into halves, quarters and eighths,
• see that half of a big whole is more than half of a small whole,
• ask half of what before comparing amounts.

Success criteria

• I can share a whole fairly among 2, 4 or 8.
• I can explain that half depends on the size of the whole.

You need

The fraction tiles (cut-out sheet 1). Two paper wholes of different sizes, one big and one small. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the fair shares. Start Session B with the two cakes and the worksheet.

Watch for these ideas

• Thinking every half is the same amount, whatever the whole.
• Comparing halves of different wholes without asking half of what.
• Losing fairness when sharing among more; the parts must stay equal.

Answers

• Shade a half of each: the big half is bigger than the small half.
• Fair shares: 2 friends get one-half each; 4 friends get one-quarter each; 8 friends get one-eighth each.
• Same or different: no. Both ate a half, but the large pie is bigger, so half of it is a larger amount.
• Draw it: the two halves are both halves but different sizes, because the wholes are different sizes.

Half of what?

A half is always half of something. Half of a big whole is more than half of a small whole.

1. Shade a half of each

Shade one half of the big cake and one half of the small cake.

The big half is ____________ than the small half.

2. Fair shares

1. 2 friends share 1 pancake equally. Each gets one-____________.
2. 4 friends share 1 pizza equally. Each gets one-____________.
3. 8 friends share 1 cake equally. Each gets one-____________.

3. Same or different?

Ana eats one-half of a small pie. Ben eats one-half of a large pie. Did they eat the same amount?

Because

4. Draw it

Draw two different wholes. Shade one half of each.

My two halves are both halves but ____________ sizes.

Fraction tiles

Cut out the tiles along the dashed lines. Line the rows up under one another: two halves cover the whole, four quarters cover the whole, and eight eighths cover the whole. Lay one one-half tile against two one-quarter tiles to see that a quarter is half of a half.

One whole

Halves (one-half each)

Quarters (one-quarter each)

Eighths (one-eighth each)

Teacher note: every row is the same length as the whole, so the tiles show at a glance that more equal parts make each part smaller. This is the same family the halving machine builds on screen.

Fold-and-cut strips

Cut out the four strips. Keep strip A whole. Fold strip B in half once, strip C in half twice, and strip D in half three times, then open them and cut along the creases.

Strip A — keep me whole (1)

Strip B — fold once, then cut: halves (1/2)

Strip C — fold twice, then cut: quarters (1/4)

Strip D — fold three times, then cut: eighths (1/8)

Equal-or-not sorting cards

Cut out the eight cards. Each whole has one cut. Sort them into two piles: equal parts (halves) and not equal (not halves). The answer key is on the Day 1 plan.

What we know: halves, quarters and eighths

Work on your own. Draw if that helps you show your thinking.

1. A ribbon is cut into 2 pieces. The two pieces are halves only when they are ____________.
2. Fill in the family. 1 whole, then 2 ____________, then 4 ____________, then 8 ____________.
3. You halve one-half of a pie. Each new piece is called a ____________.
4. You halve one-quarter. Each new piece is called an ____________.
5. An orange is cut into quarters. How many equal pieces are there? ____
6. One melon. Circle the bigger single piece: one-half or one-quarter.
7. You fold a paper strip in half, then in half again, then in half once more. How many equal parts are there now? ____
8. Mia eats one-half of a small watermelon. Jack eats one-half of a large watermelon. Did they eat the same amount? Write yes or no, and why.

Answers and marking guide

Answers

1. equal (the same size).
2. halves, quarters, eighths.
3. a quarter.
4. an eighth.
5. 4.
6. one-half.
7. 8 (eighths).
8. No. Both ate a half, but the large watermelon is bigger, so half of it is a larger amount.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, using the word equal.

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 halves, make quarters, make eighths, name and compare, and half of what.