Length, capacity and mass: 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 units, 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; they are reused all week.
4. Gather a tub of identical units (sticks, blocks, paperclips), a few cups and containers, and a balance scale or a coat-hanger.
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 finds a length by counting units; Day 2 makes those units uniform so the count can be trusted; Day 3 pours and counts capacity; Day 4 balances and counts mass; and Day 5 reaches for a smaller unit when accuracy demands it, then compares fairly. It builds on comparing and informal units from Year 1, and it opens the way to the formal units — centimetres, litres and kilograms — that arrive in Year 3.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed, and a balance scale or a coat-hanger with two cups.
• From home or the craft box: a tub of identical units to count with (paddle-pop sticks, blocks, large paperclips or dry pasta), a few small cups, and containers to fill (a jug, a bottle, a bowl).
• For pouring: water, rice or dry sand, and a tray to catch spills. Cut out once, use all week: the unit strips, the measuring worm and the cup, jug and balance cards in this pack.

Dear families

This week in maths, Year 2 measures how long, how much and how heavy things are. We use everyday units — sticks, cups and blocks — laid or poured or balanced, and we count them.

Try this at home

• Measure something long, like a bed or a table, by laying the same object end to end (shoes, books or forks) with no gaps, and count.
• Find how much a jug holds by counting cups of water as you pour them in.
• Make a balance from a coat-hanger and two cups: which piece of fruit is heavier?
• Measure one thing twice, once with a big unit and once with a small one. Which count is bigger? Which is exact?

My measures this week

Fill one row a day. Write what you measured, your unit, and how many.

Printed from the free seegongsik Length, capacity and mass teaching pack · seegongsik.com/au/y2/measurement/AC9M2M01/pack

How long? Count the units

Children find how long something is by laying one unit end to end and counting the copies. Hands come first all week: laying and counting convince faster than any rule.

We are learning to

• lay one unit end to end, with no gaps and no overlaps,
• count the units to find how long something is,
• say a length as a number and its unit, like 9 sticks.

Success criteria

• I can lay units end to end with no gaps.
• I can say how many units long something is.

You need

A tub of identical units: paddle-pop sticks, blocks or large paperclips. A few classroom objects to measure (a book, a shoe, a pencil). The unit strips (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after guess-and-lay. Start Session B by re-measuring the book, then move on to the station objects.

Watch for these ideas

• Leaving gaps between the units, or overlapping them, so the count comes out wrong.
• Starting the first unit partway along the object instead of at the very end.
• Answering with a bare number and forgetting the unit: nine sticks, not just nine.

Answers

• The ribbon on the worksheet is 8 paperclips long.
• The caterpillar drawing should be 8 blocks long, laid end to end with no gaps.
• Ben is not right: gaps leave uncounted space, so his count is wrong. Station counts vary; check each unit is laid end to end and each length is written with its unit.

Lay it and count

Choose one unit. Lay it along each object, end to end, with no gaps. Count the units and write how many. Do not forget to write the unit.

Measure these

Read the ribbon

This ribbon is measured with paperclips laid end to end. How many paperclips long is it? ____

Draw it

Draw a caterpillar that is exactly 8 blocks long. Lay the blocks end to end, with no gaps.

Think about it

Ben measured his desk but left gaps between the units. Is his count right? Write why.

One unit, no gaps

Yesterday we counted units to find a length. Today the units must all be the same size. A jumble of objects gives a number nobody can trust or repeat.

We are learning to

• see why every unit must be the same size,
• explain why a mixed count cannot be trusted,
• re-measure with one uniform unit to get a count anyone can repeat.

Success criteria

• I can say why the units must be the same size.
• I can measure with one uniform unit.

You need

Two tubs: one of mixed objects (a pencil, a peg, a block) and one of identical units. A bench or a long book to measure. The unit strips (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the mixed measure. Start Session B with same size, same answer.

Watch for these ideas

• Thinking any five objects laid in a row give a length of five.
• Believing more little units laid down must mean a longer object: units must match before counts can be compared.
• Leaving the units uneven, or mixing two sizes without noticing.

Answers

• Tim: his units are all the same size, so his count can be trusted and repeated. A block is not a pencil, so Sara’s 5 tells us nothing.
• Measured with two uniform units the number changes, because a smaller unit gives a bigger count. Both are correct for their own unit.
• Tick yes or no: Yes; No; Yes.

Same size, or it does not count

Whose count can we trust?

Tim and Sara both measured the same table. Tim used blocks that were all the same. Sara used a pencil, a rubber and a peg. Circle one: Tim or Sara. Then write why.

Measure it twice

Measure one object with two different uniform units. Write how many each time.

Did the number change when you swapped units? Write why.

Tick yes or no

Must all the units be the same size? Yes □    No □

Is it fine to mix a pencil and a block when you measure? Yes □    No □

Does a smaller unit give a bigger count? Yes □    No □

How much does it hold?

Capacity is how much a container holds. We choose one cup, pour it in again and again, and count the cups. The wide, short container often surprises them.

We are learning to

• fill a container with one chosen cup and count the cups,
• compare two containers by counting the same cup,
• see that a taller container does not always hold more.

Success criteria

• I can find how many cups fill a container.
• I can say which of two containers holds more, and by how many cups.

You need

Identical small cups or scoops. A few containers to fill (a jug, a bottle, a bowl). Water, rice or dry sand, and a tray for spills. The cup and jug cards (cut-out sheet 2). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after one cup, count as you pour. Start Session B with which holds more.

Watch for these ideas

• Thinking the taller container always holds more: height is not capacity.
• Using different-sized cups for the two containers, so the compare is unfair.
• Not filling each cup to the same level before pouring.

Answers

• Jug 9 cups and bottle 6 cups: the jug holds more, by 3 cups.
• Bowl 7 cups and mug 4 cups: least to most is the mug then the bowl; the bowl holds 3 more.
• A wide, short container can hold more than a tall, thin one, so the reason is about width, not height. Station counts vary; check the same cup is used.

Count the cups

Fill each container with the same cup. Count the cups as you pour, and write how many.

How many cups?

Which holds more?

The jug took 9 cups. The bottle took 6 cups. Which holds more? ____ How many more? ____

A bowl took 7 cups. A mug took 4 cups. Order from holds least to holds most: ____, ____

Tall is not the same as more

Draw a tall thin bottle and a short wide bowl. The bowl holds more. Show it, then write why tall does not always mean more.

How heavy? Balance it

Mass is how heavy something is. A balance scale compares: the heavier side drops. We add identical units to the other pan until the beam sits level, then count them.

We are learning to

• use a balance scale to see which object is heavier,
• add uniform units until the beam sits level,
• give a mass as a count of units, like 8 blocks.

Success criteria

• I can tell which side is heavier from a balance scale.
• I can say a mass as a number of units.

You need

A balance scale, or a coat-hanger with a cup hung on each side. A tub of identical units (blocks, glue sticks or large pasta). A few objects to weigh (a pencil case, an apple, a lunchbox). The balance cards (cut-out sheet 2). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after heavier drops. Start Session B with balance it, count it.

Watch for these ideas

• Thinking the bigger object is always heavier: a large empty box is light.
• Reading a tilted beam as if it were level.
• Forgetting the unit: the mass is eight blocks, not just eight.

Answers

• Pencil case 8 blocks and apple 12 blocks: the apple is heavier, by 4 blocks.
• The shoe is heavier than the 5 blocks, so the shoe side drops down.
• Tick yes or no: Yes; No. Station counts vary; check the beam is level before counting.

Balance and count

Put an object in one pan. Add blocks to the other pan until the beam is level. Count the blocks.

How many blocks balance it?

Which is heavier?

A pencil case balances 8 blocks. An apple balances 12 blocks. Which is heavier? ____ How many blocks more? ____

Show the tilt

Draw a balance scale. A shoe is in the left pan. It is heavier than the 5 blocks in the right pan. Show which way the beam tilts.

Tick yes or no

Does a level beam mean both sides have the same mass? Yes □    No □

Is the bigger object always the heavier one? Yes □    No □

A smaller unit, a fair compare

Sometimes a unit is too big and leaves an awkward bit. A smaller unit fits exactly. And to compare two things, both must be measured with the very same unit.

We are learning to

• choose a smaller unit when a measure is not exact,
• measure one object with two units and compare the counts,
• order lengths that share one unit, shortest first.

Success criteria

• I can pick a smaller unit when a measure leaves a bit.
• I can order lengths that use the same unit.

You need

The unit strips (cut-out sheet 1), with both the sticks and the smaller paperclips. A few objects that do not come out to a whole number of sticks. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the smaller unit. Start Session B with the fair contest and ordering.

Watch for these ideas

• Recording and a bit as if it were a measurement: a bit cannot be compared or repeated.
• Comparing counts from different units, so eight paperclips seems to beat five sticks.
• Ordering by the count without checking the unit is the same for all of them.

Answers

• The 13 paperclips measure is exact: it has no leftover bit, so the smaller unit fits the ribbon exactly.
• We cannot tell whose shoe is longer, because they used different units; measure both with the same unit to be fair.
• In order, shortest first: Blue (5), Red (8), Green (11).

Exactly, and fairly

A smaller unit for an exact answer

A ribbon is 4 sticks and a bit long. Measured in paperclips it is exactly 13. Which measure is exact? ____

Write why that measure is the exact one.

Is it a fair compare?

Mia’s shoe is 3 sticks long. Jack’s shoe is 9 paperclips long. Can we tell whose shoe is longer? ____ Write why, and what they should do.

Put them in order

Three ribbons are all measured with the same paperclips. Red is 8, Blue is 5, Green is 11. Write them in order, shortest first: ____, ____, ____

Unit strips and a measuring worm

Cut out the units. To measure a length, lay the units along the object, end to end, with no gaps, and count them. The measuring worm is a ready ruler of ten equal units: lay it down and read the length straight off.

Stick units

Paperclip units (the smaller unit)

The measuring worm

Teacher note: the stick and paperclip units are the two units from the screen. The bigger stick leaves a gap on small things, so the smaller paperclip steps in for an exact count, as in “When the unit is too big”.

Cup, jug and balance record cards

Cut out the cards. Use the cup cards as one unit for capacity (Day 3). Use the record cards to write what you poured or balanced.

Cup cards (one unit)

Capacity record cards

Balance record cards

Teacher note: the cup cards are the unit poured on screen in “Fill it with cups”, and the balance cards record the counts from “The balance scale”.

What we know: length, capacity and mass

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

1. A shelf is measured with matchsticks laid end to end, no gaps. The last one reaches 14. The shelf is ____ matchsticks long.
2. Sam measures a book with 2 blocks and 3 pencils mixed together and says it is 5 long. Can we trust his 5? Circle: yes or no. Why?
3. A jug is filled with 10 cups. A bottle is filled with 7 of the same cups. Which holds more? ____ By how many cups? ____
4. To compare how much two containers hold, you must fill them using the ____ cup (the same, or a different one?).
5. A stapler balances 9 blocks on a balance scale. The stapler has the same mass as ____ blocks.
6. On a balance scale, the side holding the heavier object goes ____ (up or down?).
7. A scarf is 8 sticks and a bit long. To measure it exactly, you should ____.
8. Three ribbons use the same sticks: Red 7, Blue 4, Green 10. Order them shortest to longest: ____, ____, ____

Answers and marking guide

Answers

1. 14 matchsticks.
2. No. The units are not the same size, so the count cannot be trusted or repeated.
3. The jug holds more, by 3 cups.
4. The same cup.
5. 9 blocks.
6. Down.
7. Measure it again with a smaller unit.
8. Blue, Red, Green (4, 7, 10).

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, counting uniform units.

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: measure length, use one uniform unit, count capacity, balance mass, and choose a smaller unit.