Length, Mass and Capacity: a week of ready-to-teach maths

Five days of lessons for Year 3 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus measuring task cards, compare 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 task cards and the compare 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. Children measure length with a ruler, mass with a scale and capacity with a measuring jug, reading each instrument’s labelled marks and working out the marks in between. Then they compare: in the same unit, or after changing one unit (1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL). The rulers, dials and jugs on the worksheets are pictures for practising reading; children measure real things with real tools.

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

Days 1 and 2 measure and compare length with a ruler. Days 3 and 4 read a scale and a jug, where the small marks between the labels need working out. Day 5 compares measurements written in different units of the same family. It leans on Measuring with Metric Units (AC9M3M01) and on Numbers Beyond 10 000 (AC9M3N01).

Materials for the week (one trip)

• From the classroom: 30 cm rulers, a metre ruler, scissors, pencils, this pack printed.
• Kitchen scales (a dial scale if you have one) and things to weigh: an apple, a stapler, a bag of rice.
• Measuring jugs, water or rice for pouring, towels, and a few containers (a cup, a mug, a bowl, a bottle).
• Strips of paper or ribbon cut to different lengths for Day 2.

Words for the word wall

ruler, scale, jug, mark, label, centimetre (cm), metre (m), gram (g), kilogram (kg), millilitre (mL), litre (L), longer, shorter, heavier, lighter, holds more, compare

Dear families

This week in maths, Year 3 is measuring with rulers, scales and measuring jugs, and comparing what they measure.

Try this at home

• Measure things in the kitchen with a ruler: a spoon, a cup, a packet. Start at 0.
• Use the kitchen scales together: which weighs more, an apple or an orange?
• When cooking, read the measuring jug at eye level: how many millilitres?
• Compare: is 1 kg of flour heavier than 800 g of sugar? How do you know?

Our measuring this week

Fill one row a day: what you measured, the tool, and the measurement with its unit.

Printed from the free seegongsik Length, Mass and Capacity teaching pack · seegongsik.com/au/y3/measurement/AC9M3M02/pack

Read the ruler

A ruler turns length into a number. Line the end of the thing up with 0, then read the labelled mark where it ends: a pencil that ends at the 7 mark is 7 cm long. Every gap between the numbered marks is 1 cm.

We are learning to

• line up the end of an object with 0 on a ruler,
• read the length at a labelled mark, in centimetres,
• measure an object that does not start at 0 by counting the centimetres between its ends.

Success criteria

• I can measure a length in centimetres with a ruler.
• I can say why we start at 0.

You need

A 30 cm ruler for each child, and a tray of short things to measure (pencils, crayons, erasers). The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the printed bars; start Session B with the real things and the hunt.

Watch for these ideas

• Starting at the end of the ruler instead of at 0. Line the object up with the 0 mark.
• Counting the marks instead of the gaps (counting 0 as 1). Count the centimetre spaces.
• Leaving off the unit (7, not 7 cm). A measurement needs its unit.

Answers

• Bars: 1. 6 cm; 2. 11 cm; 3. 3 cm; 4. 14 cm; 5. 7 cm (from 2 to 9).
• Real things: lengths vary. Check that each starts at 0 and has its unit.
• Opening: the crayon is 8 cm (from 1 to 9).

Read the ruler

How long is each bar? Look where it starts and where it ends.

Measure real things

Compare two lengths

To compare lengths fairly, line them up at the same start, or measure both in the same unit: a 15 cm string is longer than a 9 cm string, by 15 − 9 = 6 cm. Measuring lets you compare things that cannot sit side by side.

We are learning to

• compare two lengths by lining them up at the same start,
• compare by measuring both in centimetres and comparing the numbers,
• say how much longer one is, and order several lengths.

Success criteria

• I can say which is longer and by how much.
• I can order lengths from shortest to longest.

You need

Rulers, a metre ruler, and five strips of paper or ribbon of different lengths per group. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the printed bars; start Session B with the pairs and Line up.

Watch for these ideas

• Judging by where things end when they start in different places. Line the starts up first.
• Comparing numbers in different units (12 cm against 1 m). Use the same unit for both.
• Giving the longer length as “how much longer” (15 cm). Find the difference: 15 − 9.

Answers

• Printed bars: A is 8 cm and B is 7 cm, so A is longer by 1 cm, even though B ends further along.
• Pairs: the ribbon is longer by 5 cm; the hose is longer by 80 cm; the pencil is longer by 8 cm.
• Order: 9 cm, 17 cm, 23 cm, 26 cm, 31 cm.

Compare two lengths

Which bar is longer?

Bar A is ______ cm. Bar B is ______ cm. The longer bar is ______, by ______ cm.

Compare the pairs

1. A ribbon is 18 cm and a string is 13 cm. The longer one is the ______, by ______ cm.

2. A skipping rope is 160 cm and a hose is 240 cm. The longer one is the ______, by ______ cm.

3. A pencil is 17 cm and a crayon is 9 cm. The longer one is the ______, by ______ cm.

Order the lengths

Write these from shortest to longest: 23 cm, 9 cm, 31 cm, 17 cm, 26 cm

Explain

Bar B ends further along the ruler than Bar A. Why is it still shorter?

Read the scale

A kitchen scale has a needle and labelled marks. Read where the needle points: 500 g. When it stops between labels, work out what the small marks are worth: if the labels go up in 200s with one mark between, each mark is 100 g.

We are learning to

• read the mass on a dial scale with labelled markings,
• work out the value of the unlabelled marks between the labels,
• compare masses in grams, and know that 1000 g is 1 kg.

Success criteria

• I can read a mass on a scale.
• I can say what each small mark is worth.

You need

Kitchen scales (a dial one if you have it) and things to weigh: an apple, a stapler, a bag of rice. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the printed dials; start Session B with the real weighing.

Watch for these ideas

• Reading the nearest label instead of the needle (calling 700 “600”). Count the marks past it.
• Thinking every small mark is 1 g. Work it out from the labels on either side.
• Leaving off the unit, or writing kg for grams. Check the unit printed on the scale.

Answers

• Dials: A 400 g, B 700 g, C 200 g, D 900 g. Each small mark is 100 g.
• Heaviest D (900 g), lightest C (200 g); the difference is 700 g.
• A and B together: 1100 g, which is more than 1 kg (1000 g) by 100 g.

Read the scale

The labels go up in 200s. What is each small mark worth? Write each mass with its unit.

Compare

The heaviest is scale ______. The lightest is scale ______. The difference is ______ g.

Scales A and B together: ______ g. Is that more or less than 1 kg? ______

Weigh real things

Fill the jug

A measuring jug has lines labelled in millilitres. Pour, then read the line the water reaches, looking straight across at eye level: 250 mL. The 1000 mL line is 1 litre, so a litre is 1000 millilitres.

We are learning to

• read the capacity on a measuring jug with labelled lines,
• work out the value of the lines between the labels,
• compare how much containers hold, and know that 1000 mL is 1 L.

Success criteria

• I can read a capacity on a jug.
• I can say which container holds more.

You need

Measuring jugs, water (or rice or sand), a cup, a mug, a bowl and a bottle, and towels. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the printed jugs; start Session B with the containers.

Watch for these ideas

• Reading the top of the jug instead of the water. Read the line the water reaches.
• Reading from above, at an angle. Get down level with the water.
• Thinking a taller container always holds more. Measure it: the shape can fool the eye.

Answers

• Jugs: A 600 mL, B 300 mL, C 900 mL, D 200 mL. Each line between labels is 100 mL.
• Most C (900 mL), least D (200 mL); the difference is 700 mL.
• To fill jug A to 1 L: 400 mL more. Containers: answers vary; check each reading has mL.

Fill the jug

The labels go up in 200s. What is each line between them worth? Write each capacity with its unit.

Compare

Jug ______ holds the most. Jug ______ holds the least. The difference is ______ mL.

How much more water would fill jug A to 1 L? ______ mL

Measure real containers

Same family, compare

To compare measurements in different units of one family, put both in the same unit: 1 m is 100 cm, so 1 m is longer than 80 cm. A litre is 1000 mL and a kilogram is 1000 g. Choosing a sensible unit in the first place keeps the numbers easy.

We are learning to

• choose the metric unit for a measuring job (length, mass or capacity),
• know that 1 m = 100 cm, 1 kg = 1000 g and 1 L = 1000 mL,
• compare two measurements by putting them in the same unit.

Success criteria

• I can choose the right unit for a job.
• I can compare measurements written in different units.

You need

A metre ruler, a 1 L jug and a 1 kg bag of rice. The compare cards (cut-out sheet 2). The worksheet. The unit’s self-check quiz.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the card sort; start Session B with the worksheet and the quiz.

Watch for these ideas

• Comparing the numbers only (80 is more than 1, so 80 cm is longer). Use the same unit first.
• Thinking 1 L is 100 mL. A litre is 1000 mL, as a kilogram is 1000 g.
• Picking a unit from the wrong family (an apple in millilitres). Name the quantity first.

Answers

• 1 m or 90 cm: 100 cm and 90 cm, so 1 m is bigger; 750 mL or 1 L: 750 mL and 1000 mL, so 1 L is bigger; 3 kg or 2500 g: 3000 g and 2500 g, so 3 kg is bigger; 60 cm or 1 m: 60 cm and 100 cm, so 1 m is bigger; 1 L or 1200 mL: 1000 mL and 1200 mL, so 1200 mL is bigger; 1 kg or 800 g: 1000 g and 800 g, so 1 kg is bigger.
• Units: the water in a bath L; the mass of a pencil g; the length of a car m; a cup of milk mL. Order: 400 g, 1 kg, 1500 g.

Same family, compare

Which is bigger?

Put both in the same unit first. 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL.

Pick the unit

Order the masses

Lightest to heaviest: 1 kg, 400 g, 1500 g  →  ______________________________

Measuring task cards

Cut out the twelve cards and set them out as stations: length cards with rulers, mass cards with the scales, capacity cards with the jugs and water. Groups record each answer with its unit.

Teacher note: answers depend on your classroom things. Check that each child starts at 0, reads at eye level, and writes the unit.

Compare cards

Cut out the twelve cards. On Day 5, pairs put both measurements on each card into the same unit, then sort the cards into “first is bigger”, “second is bigger” and “the same”.

Teacher note: 1 m or 75 cm: 1 m is bigger; 400 mL or 1 L: 1 L is bigger; 2 kg or 1800 g: 2 kg is bigger; 1 L or 900 mL: 1 L is bigger; 50 cm or 1 m: 1 m is bigger; 1 kg or 1200 g: 1200 g is bigger; 2 m or 150 cm: 2 m is bigger; 3 L or 2500 mL: 3 L is bigger; 700 g or 1 kg: 1 kg is bigger; 1 m or 100 cm: the same; 1 kg or 1000 g: the same; 250 mL or 1 L: 1 L is bigger.

What we know: Length, Mass and Capacity

Work on your own. Write a unit with every measurement.

1. How long is the bar? ______
2. How long is this bar? ______
3. A ribbon is 24 cm and a string is 31 cm. Which is longer, and by how much? ______________________
4. What mass does the scale show? ______
5. How much water is in the jug? ______
6. Circle the unit. The water in a bath: mL / L    The mass of a pencil: g / kg
7. Which holds more, 1 L or 800 mL? ______ Why? ______________________
8. Order from lightest to heaviest: 2 kg, 500 g, 1500 g. ______________________________

Answers and marking guide

Answers

1. 9 cm.
2. 8 cm (from 3 to 11).
3. The string, by 7 cm (31 − 24).
4. 700 g.
5. 400 mL.
6. L; g.
7. 1 L, because 1 L is 1000 mL, which is more than 800 mL.
8. 500 g, 1500 g, 2 kg (2000 g).

A quick three-level guide

Eight questions, three ideas. A child at standard reads each instrument, including the marks between the labels, and compares in the same unit.

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: reading a ruler, comparing lengths, reading a scale, reading a jug, and comparing across units.