Converting Metric Units: a week of ready-to-teach maths

Five days of lessons for Year 6 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus I have, who has loop cards for the class, thing and unit cards for pairs, 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 I have, who has cards once for the class, and the thing and unit cards once for each pair.
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. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: converting changes the unit and the number, never the amount. Metric units climb in tens: 10 mm make a centimetre, 100 cm make a metre and 1000 m make a kilometre, and the same thousand links grams and kilograms, kilograms and tonnes, and millilitres and litres. Stepping down to a smaller unit takes more of them, so you multiply; stepping up takes fewer, so you divide. Every step is a power of ten, so the digits stay as they are and only the decimal point moves.

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.

Words to watch

Kilo means a thousand and milli means a thousandth, whatever unit they are joined to: a kilogram is 1000 g and a millilitre is a thousandth of a litre. Centi means a hundredth. A tonne is 1000 kg. Unit symbols take no full stop and no s, and a space separates the number from its symbol: 2.5 kg, not 2.5kgs.

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 steps lengths up and down the staircase of units; Day 2 shows that converting only moves the point; Day 3 carries the same thousand to mass and capacity; Day 4 chooses the unit and the decimal that suit the context; and Day 5 solves problems that mix units. It builds on the Year 5 work of choosing units and combining two units (AC9M5M01) and on decimals to thousandths (AC9M5N01). It leads to the area of rectangles (AC9M6M02), where both lengths must be in the same unit, and to the Year 7 work on area and volume in appropriate units.

Materials for the week (one trip)

• From the classroom: 30 cm rulers, metre rulers or tape measures, scissors and this pack printed.
• If you have them: kitchen scales and measuring jugs with some water for Day 3.
• From home: empty food packets and drink bottles with the amount on the label, for Day 3.
• Cut out once: the I have, who has cards (one set for the class) and the thing and unit cards (one set per pair).

Words for the word wall

millimetre (mm), centimetre (cm), metre (m), kilometre (km), gram (g), kilogram (kg), tonne (t), millilitre (mL), litre (L), convert, decimal point, place value, estimate, sensible

Dear families

This week in maths, Year 6 converts between metric units of length, mass and capacity, such as 1.5 km = 1500 m and 750 mL = 0.75 L, and chooses the unit that suits each job. Please send in an empty food packet or drink bottle with the amount on the label for Wednesday.

Try this at home

• Read the labels in the pantry and say each amount in the other unit: 500 g is 0.5 kg.
• Measure a few things with a tape measure and say each length in two units.
• Pour a 2 L bottle of water into 250 mL cups. How many cups does it fill?
• On a drive or a walk, guess the distance in kilometres, then check it on a map.

Our measurements this week

Fill one row a day. Write something you measured or read, the amount, and the same amount in another unit.

Printed from the free seegongsik Converting Metric Units teaching pack · seegongsik.com/au/y6/measurement/AC9M6M01/pack

Up and down the staircase

Units of length climb in tens: 10 mm make 1 cm, 100 cm make 1 m and 1000 m make 1 km. Stepping down to a smaller unit takes more of them, so you multiply; stepping up takes fewer, so you divide. Children measure real things in two units, step lengths up and down the staircase, and compare lengths written in different units.

We are learning to

• measure a length and write it in two units,
• convert between mm, cm, m and km by multiplying or dividing by 10, 100 or 1000,
• compare lengths written in different units.

Success criteria

• I can say why 3 m is 300 cm but only 0.003 km.
• I can tell which is longer, 1.2 m or 115 cm, and show how I know.

You need

The worksheet, one per child, a 30 cm ruler each, and a metre ruler or tape measure for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the staircase tables in Part B.

Watch for these ideas

• Multiplying when stepping up to a bigger unit, so 250 cm becomes 25 000 m.
• Using 100 for every step, when m to km is 1000 and cm to mm is 10.
• Comparing the numbers and not the lengths: 450 mm is not longer than 0.5 m.

Answers

• Part A: lengths vary. The mm number is 10 times the cm number (a 17.5 cm pencil is 175 mm), the cm number is 100 times the m number, and the m number is 1000 times the km number.
• Part B: 2400 mm = 240 cm = 2.4 m; 85 mm = 8.5 cm = 0.085 m; 1600 mm = 160 cm = 1.6 m; 70 mm = 7 cm = 0.07 m; 1250 mm = 125 cm = 1.25 m; 600 mm = 60 cm = 0.6 m. 3500 m = 3.5 km; 2000 m = 2 km; 400 m = 0.4 km; 12 500 m = 12.5 km; 75 m = 0.075 km; 8050 m = 8.05 km.
• Part C, the longer one: 1.2 m (115 cm is 1.15 m); 0.5 m (450 mm is 0.45 m); 2500 m (2.05 km is 2050 m); the same; 0.8 m (75 cm is 0.75 m); 3 km (2999 m is 2.999 km).

Up and down the staircase

A. Measure it twice

Measure each thing, then write the same length in the second unit without measuring again.

B. Up and down the staircase

C. Which is longer?

Write both lengths in the same unit, then circle the longer one. If they are the same, write “same”.

Move the point

Every step between units is 10, 100 or 1000, so converting never changes the digits; it only moves them past the point. In a place-value chart for metres, kilometres sit in the thousands column, centimetres in the hundredths and millimetres in the thousandths, so a length reads in any unit with the point just after that unit’s column. Children use the chart, convert without it, and check conversions for size.

We are learning to

• use a place-value chart to convert between units of length,
• convert lengths written as decimals, such as 2.3 km and 0.75 km,
• check a conversion by asking whether the number should get bigger or smaller.

Success criteria

• I can write 4.05 km in metres and explain the 0 in 4050 m.
• I can find the slip in 3.5 km = 350 m.

You need

The worksheet, one per child, and the I have, who has cards (cut-outs), one set for the class.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the conversions in Part B.

Watch for these ideas

• Moving the point the wrong way, so 750 m becomes 750 000 km.
• Moving the point 2 places between metres and kilometres, as if every step were 100.
• Losing a zero that holds a place: 4.05 km is 4050 m, not 405 m.

Answers

• Part A: 2300 m, 0.75 km, 4050 m, 125 cm, 0.006 m, 400 mm. Each time the point sits just after the column of the unit you want.
• Part B: 3750 m, 0.82 km, 900 m, 0.055 km, 14 km, 260 cm, 1.45 m, 0.09 m, 3.7 cm, 62 mm.
• Part C: Sam moved the point 2 places, not 3: 3500 m; Kai moved the point 1 place, not 2: 0.62 m; Riley is right; Jordan moved the point 2 places, not 3: 4050 m.

Move the point

A. Use the chart

One digit to a box, with the whole number of the given unit in its own column: for 2.3 km, the 2 goes under km and the 3 just right of it. To read the new unit, put the point just after its column and fill empty boxes up to the point with zeros.

The thick line is where the point sits for metres.

B. Convert without the chart

C. Spot the slip

Tick each conversion that is right. Fix each one that is wrong and say how far the point should move.

Sam wrote 3.5 km = 350 m.  ____________________________________________

Kai wrote 62 cm = 6.2 m.  ____________________________________________

Riley wrote 750 mm = 0.75 m.  ____________________________________________

Jordan wrote 4.05 km = 405 m.  ____________________________________________

Mass and capacity

Mass and capacity use the same thousand as length: 1 kg is 1000 g, 1 t is 1000 kg and 1 L is 1000 mL, so the point moves three places each time. Children read jugs and scales and write each reading in both units, change the amounts on food labels, and compare masses and capacities given in different units.

We are learning to

• read a jug or a scale and write the reading in two units,
• convert between grams, kilograms and tonnes, and between millilitres and litres,
• compare masses and capacities written in different units.

Success criteria

• I can read 650 mL on a jug and write it as 0.65 L.
• I can say which is heavier, 0.8 kg or 750 g, and why.

You need

The worksheet, one per child; kitchen scales, jugs and water if you have them; the food packets from home; and the I have, who has cards.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the real packets and Part B.

Watch for these ideas

• Counting each small mark as 1 or 10 without working out the gap between the labels.
• Writing 1.3 L as 130 mL, moving the point two places instead of three.
• Comparing the numbers, not the amounts: 750 g is less than 0.8 kg.

Answers

• Part A: (A) 650 mL = 0.65 L, each small mark 50 mL; (B) 1.3 L = 1300 mL, each small mark 0.1 L; (C) 1.7 kg = 1700 g, each small mark 0.1 kg; (D) 380 g = 0.38 kg, each small mark 10 g.
• Part B: rice 1500 g, cereal 0.725 kg, milk 2000 mL, juice box 0.25 L, yoghurt tub 0.17 kg, sparkling water 1250 mL.
• Part C, the larger amount: 0.8 kg (750 g is 0.75 kg); 1250 mL (1.2 L is 1200 mL); 2.5 t (2400 kg is 2.4 t); 0.45 kg (405 g is 0.405 kg); the same; 650 mL (0.6 L is 600 mL).

Mass and capacity

A. Read each jug and each scale

Work out what each small mark is worth first. Write the reading in the unit shown, then in the other unit.

B. Change the label

C. Which is more?

Write both amounts in the same unit, then circle the larger one. If they are the same, write “same”.

The unit that fits

A measurement can be written in any unit, but the context decides which reads best: a bus trip in kilometres, an ant in millimetres, a teaspoon in millilitres. The unit that fits keeps the number a sensible size, with no long string of zeros. Children rewrite clumsy measurements, write two-unit measurements as one decimal, and order measurements given in mixed units.

We are learning to

• choose a unit that keeps the number a sensible size,
• write a measurement such as 4 km 50 m as one decimal,
• order measurements given in different units.

Success criteria

• I can rewrite 0.004 m in a unit that fits.
• I can write 4 km 50 m as 4.05 km and explain the 0.

You need

The worksheet, one per child, and the thing and unit cards (cut-outs), one set per pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the two-unit measurements in Part B.

Watch for these ideas

• Reading 4 km 50 m as 4.5 km, because 50 looks like a half.
• Keeping a unit that makes a long string of zeros, such as 86 000 m.
• Ordering by the numbers alone, so 990 g looks heavier than 1.05 kg.

Answers

• Part A: 86 km, 4 mm, 5 mL, 3.5 kg, 32 m, 9 t.
• Part B: 3.45 m, 2.3 kg, 1.25 L, 4.05 km, 3.085 kg, 2.05 m.
• Part C: long jumps 3050 mm, 315 cm, 3.2 m, 3.25 m; pumpkins 990 g, 1.05 kg, 1100 g, 1.2 kg; drinks 0.55 L, 580 mL, 0.6 L, 650 mL.

The unit that fits

A. Make it sensible

Rewrite each measurement in a unit that fits, so the number is a sensible size.

1. The bus trip to camp is 86 000 m long.  ____________________

2. The ant is 0.004 m long.  ____________________

3. A teaspoon holds 0.005 L of medicine.  ____________________

4. The watermelon has a mass of 3500 g.  ____________________

5. The school hall is 0.032 km long.  ____________________

6. The truck carries 9000 kg of sand.  ____________________

B. One unit, as a decimal

Write each measurement in the larger unit, as a decimal.

C. Put them in order

Write all four in the same unit first.

Convert to solve

Real problems mix units: the recipe says grams and the bag says kilograms. Children estimate first, write every amount in one unit, solve, then check that the answer is a sensible size and give it in the unit the question asks for.

We are learning to

• write every amount in one unit before adding, comparing or sharing,
• solve problems that mix units,
• check that an answer is a sensible size and in the unit the question asks for.

Success criteria

• I can find how many 600 mL bottles a 4.5 L cooler fills.
• I can say whether a 2 kg post bag takes all three things, and by how much.

You need

The worksheet, one per child, and calculators for checking if you wish.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first three problems in Part A; start Session B with the cooler.

Watch for these ideas

• Adding amounts in different units as if they matched: 750 g and 0.6 kg make 1350 g, not 750.6 g.
• Giving a part of a bottle or a piece when the question asks how many are full.
• Leaving an answer in the wrong unit, or skipping the check that it is a sensible size.

Answers

• Part A: (1) 6500 mL = 6.5 L; (2) 1600 m = 1.6 km; (3) 1750 g = 1.75 kg is needed, so no: 250 g short; (4) 7 bottles, with 300 mL left; (5) 1830 g = 1.83 kg, so yes: 170 g under; (6) 3 pieces, with 25 cm left.
• Part B: Sam’s answer is 10 times too big: 18 L; Kai is right; Riley is right; Jordan’s answer is 10 times too big: 12 m.

Convert to solve

A. Estimate, then solve

Estimate first. Then write the amounts in one unit, solve, and give the answer in the unit the question asks for.

B. Check the size

Is each answer a sensible size? Tick it if it is right. If it is not, fix it.

Sam worked out that 12 bottles of 1.5 L hold 180 L.  ______________________

Kai worked out that 8 laps of a 400 m track make 3.2 km.  ______________________

Riley worked out that a 2 kg bag of flour less 450 g leaves 1.55 kg.  ______________________

Jordan worked out that 5 planks of 2.4 m laid end to end make 120 m.  ______________________

I have, who has

Cut out the twenty-four cards once, one set for the class.

I have, who has (Days 2 and 3)

1. Deal out all the cards. Some children may hold two; a pair can share one.
2. Anyone starts by reading their card aloud: “I have … Who has …?”
3. The child holding the same amount in a different unit reads their card next. Keep going until the loop comes back to the start.

Teacher note: the cards make one loop, so any card can start. In order: 1.5 km, 250 g, 0.75 L, 320 cm, 45 mm, 2.05 kg, 600 mL, 1.25 m, 3 t, 40 cm, 2400 m, 0.08 L, 375 g, 9 mm, 4.2 L, 0.065 km, 1500 kg, 0.006 m, 1250 mL, 0.5 kg, 12 cm, 3.6 km, 50 g, 2.5 L, then back to the first. Time the class and play again to beat it.

Thing cards and unit cards

Cut out the sixteen thing cards and the nine unit cards once, one set for each pair.

Fit the unit (Day 4)

1. Lay the unit cards face up between you. Shuffle the thing cards face down.
2. Turn over a thing card. Both players race to touch the unit that fits it.
3. To win the card, the first to touch must say a sensible size in that unit, and the other player must agree.

Teacher note, the unit that fits each thing: the length of a bee, mm; the thickness of a coin, mm; the length of a pencil case, cm; the width of a book, cm; the height of a netball ring, m; the length of a swimming pool, m; the length of a marathon, km; the drive from Sydney to Melbourne, km; the mass of a tennis ball, g; the mass of a sheet of paper, g; the mass of a bag of potatoes, kg; the mass of a dog, kg; the mass of a loaded truck, t; the water in a teaspoon, mL; the water in a bath, L; the milk in a carton, L.

What we know: Converting Metric Units

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

1. 3.2 m = ______ cm
2. 4500 g = ______ kg
3. 0.6 L = ______ mL
4. 2.04 km = ______ m
5. Write 5 kg 70 g in kilograms. ______
6. Order from lightest to heaviest: 1.2 kg, 1050 g, 0.95 kg. ______________________________
7. The bike ride was 45 000 m. Write it in a unit that fits. ______
8. A 2 L jug of water fills cups of 250 mL. How many cups does it fill? ______

Answers and marking guide

Answers

1. 320 cm.
2. 4.5 kg.
3. 600 mL.
4. 2040 m.
5. 5.07 kg (the 0 keeps the 7 in the hundredths place: 70 g is 0.07 kg).
6. 0.95 kg, 1050 g, 1.2 kg.
7. 45 km.
8. 8 cups (2000 mL ÷ 250 mL).

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say which way the point moves, and how far, for each conversion.

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: lengths up and down the staircase, moving the point, mass and capacity, the unit that fits, and solving problems.