Halves and Quarters Around Us: a week of ready-to-teach maths
Five days of lessons for Year 2 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out fraction shapes, clock faces and collection cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the two card sheets once; they are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and when.
- 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.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Half is two equal parts | Fold and cut shapes and objects into two matching halves | The sandwich cut |
| 2 | Quarters are four equal parts | Make four equal parts of shapes and objects, and count quarters | Orange quarters |
| 3 | Eighths: halve it again | Halve a quarter to make eighths, and compare the pieces | The sandwich cut |
| 4 | Halves and quarters of time | Find half and a quarter of an hour, and the parts of a match | The hour circle |
| 5 | A fair share of a collection | Judge fair and unfair shares, then halve and quarter a group | Fair cut or foul? |
How the week builds
Day 1 makes two equal halves; Day 2 halves again for quarters; Day 3 halves once more for eighths; Day 4 cuts time and a match into the same parts; and Day 5 shares a group fairly. It builds on the Number fractions unit, where children first folded and halved, and it opens the way to reading the clock, where half past and quarter past live.
Materials for the week (one trip)
- From the classroom: scissors, pencils, counters or dry pasta, this pack printed.
- From home or the kitchen (handy but not needed): an orange or an apple to cut, a round cracker or paper plate, a wall clock or toy clock to point to.
- Cut out once, use all week: the fraction strips and shapes, the clock faces and the collection cards in this pack. No maths equipment to buy.
Dear families
This week in maths, Year 2 finds halves, quarters and eighths all around us: in shapes we cut, objects we share, and events like an hour or a match. The one big idea is that the parts must be equal.
Try this at home
- Cut something in half at snack time: a sandwich, an apple, a piece of toast. Are the two parts equal? That is what makes them halves.
- Quarter it: cut each half in half again. Four equal parts are quarters; eight are eighths.
- Talk about time: half an hour of reading, a quarter of an hour to tidy up. Point to the clock and watch the minute hand.
- Share a collection fairly: half the grapes each for two, a quarter of the strawberries each for four.
My fair shares this week
Fill one row a day. Tick when the parts were really equal.
| Day | What I cut or shared | Equal parts | Each part is a ___ |
|---|---|---|---|
| Monday | □ | ||
| Tuesday | □ | ||
| Wednesday | □ | ||
| Thursday | □ | ||
| Friday | □ |
Printed from the free seegongsik Halves and Quarters Around Us teaching pack · seegongsik.com/au/y2/measurement/AC9M2M02/pack
Half is two equal parts
Half means two equal parts. Today children fold and cut shapes and objects into two parts that match exactly, and learn that a half can look like a different shape and still be a half.
We are learning to
- make two equal parts of a shape or object,
- check that two parts are really halves by matching them,
- see that the same half can be a different shape.
Success criteria
- I can fold or cut a shape into two equal parts.
- I can say whether two parts are halves.
You need
The fraction strips and fold-and-cut shapes (cut-out sheet 1), one set per pair. Scissors. A round cracker, a paper plate or a sandwich to halve, if you have one. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fold it fair Each child folds a paper square or circle once so the two parts sit exactly on top of each other. Ask: “How do you know your two parts are equal? Fold and check that one lies right on top of the other.” |
| 30 min | Two halves, two shapes Cut a square sandwich straight down for two rectangles, then a fresh one corner to corner for two triangles. Both give halves. Children fold and cut their own shapes, then match the parts. Ask: “The triangle looks longer than the rectangle. Is it more than half? Lay the two pieces on top of each other and tell me.” |
| 10 min | Half or not? Show some pieces cut off-centre. Children give a thumb up for halves, a thumb down for not. Ask: “These two parts are not the same size. Can we call them halves? Why not?” |
Two half-sessions instead? End Session A after the folding. Start Session B by cutting the sandwich the two ways and matching the pieces.
Watch for these ideas
- Calling any two pieces halves: two parts are halves only when they are equal.
- Thinking the triangle half is bigger than the rectangle half because it looks longer: matching the pieces settles it.
- Cutting a little off-centre and still saying half: line the parts up to check.
Answers
- A straight cut gives two rectangles; a corner-to-corner cut gives two triangles. Both are halves.
- Half or not half: the straight cut is halves; the lopsided circle is not halves; the fold that matches is halves.
- Two parts are halves only when they are equal, so the missing word is equal (the same size).
Cut it in half
Show two equal parts. Fold, cut and match to check the two parts are really halves.
Fold and colour
Take a fold-and-cut shape from the cut-out sheet. Fold it into two equal parts. Open it and colour one half. Draw it here.
Two halves, two shapes
A sandwich can be halved two ways. Draw it cut into two rectangles, then draw it cut into two triangles.
Half or not half?
Tick whether each cut makes two halves.
| The cut | Two halves? |
|---|---|
| A square cut straight down the middle into two matching parts | Yes □ No □ |
| A circle cut so one part is much bigger than the other | Yes □ No □ |
| A shape folded so the two sides land right on top of each other | Yes □ No □ |
Quarters are four equal parts
A quarter is one of four equal parts. Halve a shape, then halve each half, and you have quarters. Today children make quarters of shapes and objects, and count how quarters add up in fours.
We are learning to
- make four equal parts of a shape or object,
- name one of four equal parts as a quarter,
- count quarters: four quarters make a whole, eight make two wholes.
Success criteria
- I can cut or fold something into four equal parts.
- I can say that four quarters make one whole.
You need
The fraction strips and fold-and-cut shapes (cut-out sheet 1). An orange or a round cracker to quarter, if you have one. Scissors. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Halve the half Children take a half from a folded shape and fold it again. Four equal parts appear. Ask: “You folded once for halves. Fold again. How many equal parts now, and what do we call one of them?” |
| 30 min | Quarter the orange Cut an orange or a paper circle in half, then each half in half: four quarters. Count for the team: one orange is four quarters, two oranges are eight. Children quarter their own shapes and count. Ask: “One orange gives four quarters. How many quarters would two oranges give? Count in fours with me.” |
| 10 min | Show me a quarter Children hold up one quarter of a fraction strip; the class checks the parts are equal. Ask: “Is this really a quarter? How many of these pieces would rebuild the whole strip?” |
Two half-sessions instead? End Session A after folding into quarters. Start Session B by quartering the orange and counting.
Watch for these ideas
- Making four parts that are not equal and still calling them quarters.
- Thinking a quarter must be a corner square: a quarter is any one of four equal parts, whatever its shape.
- Losing count of the quarters: four quarters always rebuild one whole.
Answers
- One orange gives 4 quarters; two oranges give 8; three give 12; four give 16.
- Four quarters make one whole, and two quarters make one half.
- Worksheet drawings vary: check each shape is cut into four equal parts.
Make quarters
Four equal parts are quarters. Fold, cut, count and colour to show quarters.
Fold into quarters
Take a fold-and-cut shape. Fold it into four equal parts. Open it and colour one quarter. Draw it here.
Colour one quarter
This bar has four equal parts. Colour one quarter.
Count the quarters
Each orange is cut into four quarters. Fill in the quarter pieces.
| Oranges | Quarter pieces |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 |
Finish the sentences
Four quarters make one ____________.
Two quarters make one ____________.
Eighths: halve it again
Halve a quarter and you get an eighth. Today children make eighths by halving one more time, and see the surprise underneath: the more equal parts you make, the smaller each part becomes.
We are learning to
- make eight equal parts by halving a quarter,
- name one of eight equal parts as an eighth,
- see that more parts means smaller parts.
Success criteria
- I can fold a shape into eighths by halving three times.
- I can say that eight eighths make one whole.
You need
The fold-and-cut shapes and the fraction strips (cut-out sheet 1). Scissors. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Halve, halve, halve Fold a shape in half, then in half again, then once more. Count the parts after each fold: two, four, eight. Ask: “Each fold doubles the parts: two, four, eight. What do we call eight equal parts?” |
| 30 min | Line up the strips Lay the whole strip, the halves, the quarters and the eighths one under another. Match them: two eighths cover one quarter, two quarters cover one half. Ask: “How many eighths cover one quarter? Lay them on top of each other and count.” |
| 10 min | Bigger or smaller? Compare one half, one quarter and one eighth of the same strip. Which piece is biggest? Ask: “We made more pieces, but each piece got bigger or smaller? Tell me why.” |
Two half-sessions instead? End Session A after folding to eighths. Start Session B by lining up the strips to compare.
Watch for these ideas
- Thinking an eighth is bigger than a quarter because eight is bigger than four: more parts means smaller parts.
- Uneven folds giving pieces that are not really eighths.
- Forgetting that all eight pieces come from one whole.
Answers
- Fold three times: 2, then 4, then 8 equal parts. Eight equal parts are eighths.
- 2 eighths cover one quarter; 4 eighths cover one half; 8 eighths make one whole.
- Of the same cake, one half is the biggest piece, then one quarter, then one eighth is the smallest.
Make eighths
Halve, then halve, then halve again. Count the parts and see them shrink.
Halve it again and again
Fill in how many equal parts each fold makes, and the name of one part.
| Folds | Equal parts | Name of one part |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 |
Cover the whole
____ eighths make one quarter.
____ eighths make one half.
____ eighths make one whole.
Colour one eighth
This bar has eight equal parts. Colour one eighth.
Which piece is biggest?
These are all pieces of the same cake. Ring the biggest piece: one half, one quarter, one eighth.
Halves and quarters of time
Time can be cut into halves and quarters too. Half an hour is 30 minutes; a quarter of an hour is 15. A footy match is one whole made of four quarters. Today the fractions step off the plate and onto the clock and the scoreboard.
We are learning to
- say how many minutes are in half an hour and a quarter of an hour,
- name the parts of a match: quarter-time, half-time and three-quarter-time,
- see an event as a whole that is cut into equal parts.
Success criteria
- I can say that half an hour is 30 minutes and a quarter of an hour is 15.
- I can point to half-time on a match made of four quarters.
You need
The clock faces and the match bar (cut-out sheet 2). A toy clock or a wall clock to point to. Coloured pencils. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Sweep the hour Point to the clock. The minute hand going all the way round is one hour, 60 minutes; halfway round is half an hour. Ask: “The hand has swept halfway round. How many minutes is that, and how do you know?” |
| 30 min | Clocks and quarters Children shade half and a quarter of a paper clock and label 30 and 15 minutes. Then they mark quarter-time, half-time and three-quarter-time on the match bar. Ask: “The match has four quarters. Which mark is half-time, and how many quarters have been played by then?” |
| 10 min | Name the time Show a quarter turn and a half turn of the minute hand; children call out the minutes. Ask: “A quarter of an hour has gone by. Where is the minute hand, and how many minutes is that?” |
Two half-sessions instead? End Session A after shading the clocks. Start Session B with the match bar.
Watch for these ideas
- Thinking half an hour is 50 minutes because half of 100: an hour is 60 minutes, and half of 60 is 30.
- Reading a quarter of an hour as 25 minutes: a quarter of 60 is 15.
- Thinking half-time is one quarter in: half-time is two quarters, halfway through the match.
Answers
- Half an hour is 30 minutes; a quarter of an hour is 15 minutes; a whole hour is 60 minutes.
- Three quarters of an hour is 45 minutes.
- On a four-quarter match: quarter-time is after 1 quarter, half-time after 2, three-quarter-time after 3.
Halves and quarters of time
An hour and a match are wholes too. Cut them into halves and quarters.
Minutes in an hour
One hour is 60 minutes. Fill in the minutes.
| How much of an hour | Minutes |
|---|---|
| A whole hour | 60 |
| Half an hour | |
| A quarter of an hour | |
| Three quarters of an hour |
Shade the clock
Take two clock faces from the cut-out sheet. Shade half of one clock and write 30 minutes beside it. Shade a quarter of the other and write 15 minutes.
The match bar
This match has four quarters. Draw an arrow to quarter-time, half-time and three-quarter-time.
Half-time is after ____ quarters. Three-quarter-time is after ____ quarters.
A fair share of a collection
A fraction of a group works the same way as a fraction of a shape: the parts must be equal. Today children judge fair and unfair shares, then find half of a class and a quarter of a collection like a carton of eggs.
We are learning to
- judge whether a share is fair, with equal groups,
- find half of a small collection,
- find a quarter of a collection.
Success criteria
- I can say whether a share into halves or quarters is fair.
- I can find half and a quarter of a group of objects.
You need
The collection cards (cut-out sheet 2). Counters or dry pasta to share out. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fair or foul? Share 8 counters between two children two ways: 4 and 4, then 6 and 2. Children judge each share. Ask: “Both shares used all eight counters. Which one made two equal halves, and why is the other one not halves?” |
| 30 min | Half the class, a quarter of the eggs Deal a collection into equal groups. Half of 8 is 4; a quarter of 8 is 2, shared into four equal groups. Children use counters and the collection cards. Ask: “To find a quarter, into how many equal groups do we share, and how many are in one group?” |
| 10 min | Share it fairly Give a small collection; children halve it, then quarter it by sharing each half again. Ask: “You found half. Now share each half again. What fraction of the whole is one group now?” |
Two half-sessions instead? End Session A after judging fair and foul shares. Start Session B by halving and quartering a collection.
Watch for these ideas
- Sharing a collection into unequal piles and still calling them halves or quarters.
- Finding a quarter by sharing into two groups instead of four.
- Thinking half of a group means half of one object, not half of the count.
Answers
- Half of 8 is 4; half of 10 is 5; half of 6 is 3.
- A quarter of 8 is 2; a quarter of 12 is 3, shared into four equal groups.
- Fair or foul: 4 and 4 is fair; 6 and 2 is not; four equal groups of 3 is fair; 4, 4, 3 and 1 is not.
A fair share
A fair share has equal parts. Judge the shares, then halve and quarter a group.
Fair or foul?
Tick whether each share is fair, with equal parts.
| The share | Fair share? |
|---|---|
| 8 apples shared 4 and 4 | Yes □ No □ |
| 8 apples shared 6 and 2 | Yes □ No □ |
| 12 pencils shared into four equal groups of 3 | Yes □ No □ |
| 12 pencils shared into groups of 4, 4, 3 and 1 | Yes □ No □ |
Half of a group
Half of 8 children is ____.
Half of 10 apples is ____.
Half of 6 grapes is ____.
A quarter of a collection
Here are 8 eggs. Share them into four equal groups and ring one quarter.
A quarter of 8 eggs is ____. A quarter of 12 pencils is ____.
Fraction strips and shapes
Cut out the four strips. They are all the same length. Line them up one under another to see how the parts compare: two eighths cover one quarter, two quarters cover one half.
Fraction strips (cut along the lines)
Teacher note: this is the same idea the sandwich cut shows on screen, with the pieces held still so children can match them.
Fold-and-cut shapes
Cut out each shape. Fold it in half, then in half again for quarters, then once more for eighths. Each fold makes matching parts.
Teacher note: the square is the sandwich from Day 1, the circle is the orange from Day 2, and any shape folds down to eighths on Day 3.
Clock faces and collection cards
Cut out the clock faces to shade halves and quarters of an hour (Day 4). Cut out the match bar to mark the breaks (Day 4). Cut out the collection cards to halve and quarter a group (Day 5).
Clock faces (shade the fraction, then draw the hands)
Match bar
One whole match, four quarters. Mark quarter-time, half-time and three-quarter-time.
Collection cards
Each card is a group to share. Ring one half, then ring one quarter.
Teacher note: half of the 8-card is 4, a quarter of the 8-card is 2, and a quarter of the 12-card is 3, shared into four equal groups.
What we know: halves, quarters and eighths
Work on your own. Draw or write your thinking if you can.
- A pizza is cut into 2 equal pieces. Each piece is one ____.
- A ribbon is folded into 4 equal parts. Each part is one ____.
- A chocolate bar is broken into 8 equal pieces. Each piece is one ____.
- ____ eighths make one half.
- Two parts of a shape are halves only when they are ____.
- A quarter of an hour is ____ minutes. Three quarters of an hour is ____ minutes.
- Two children share 10 stickers: one gets 7 and one gets 3. Are these two halves? Yes □ No □
- Half of 8 eggs is ____. A quarter of 8 eggs is ____.
Answers and marking guide
Answers
- half.
- quarter.
- eighth.
- 4 eighths make one half.
- equal (the same size).
- 15 minutes; 45 minutes.
- No: 7 and 3 are not equal, so they are not halves.
- Half of 8 is 4; a quarter of 8 is 2.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Name the fraction (Q1, Q2, Q3) | names a half of a shape | names halves, quarters and eighths of shapes and objects | explains that the name comes from the number of equal parts |
| Equal parts (Q4, Q5, Q7) | sees when two parts look equal | knows the parts must be equal, and how eighths, quarters and halves relate | explains why unequal pieces are not fractions |
| Fractions of time (Q6) | knows half an hour is 30 minutes | finds a quarter and three quarters of an hour in minutes | links the clock sweep to the fraction |
| Fractions of a collection (Q8) | halves a small group | finds half and a quarter of a collection | shares a group into four equal groups and names one |
Eight questions, four ideas. A child at standard names the fractions and shares a group into equal parts, and can say why.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Halves of shapes | Quarters | Eighths | Time and events | Fair shares |
|---|---|---|---|---|---|
The five columns are the five days: halve a shape, make quarters, make eighths, fractions of time, and a fair share of a group.