Teaching pack: Measuring with Informal Units (Year 1) -- a week of maths lessons

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Teaching pack · Year 1 Measurementseegongsik /au

Measuring with informal units: a week of maths

Five days of lessons for Year 1 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out unit strips, a mini-check and every answer.

AC9M1M02

measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end

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 unit strips once; they are the same-size units children lay 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 muddles 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 40 minutes a day. Run them in order: Day 1 lays units end to end, Days 2 and 3 fix the two rules (no gaps, all the same size), Day 4 shows a bigger unit gives a smaller number, and Day 5 uses one shared unit to compare two things.

On the board

This pack is the printable half of a free interactive unit. The on-screen half has five interactive pictures — “Lay them end to end”, “The gap trap”, “Mixed-up units”, “Big units, small numbers” and “Whose desk is longer?” — plus a self-check quiz you can run as a class game on Day 5.

seegongsik.com/au/y1/measurement/AC9M1M02

Aligned to the Australian Curriculum V9 (AC9M1M02). This pack is original material from seegongsik, independently produced and not endorsed by ACARA. Curriculum content descriptors are (c) ACARA, licensed under CC BY 4.0. Free to print and use in class.

The week at a glance5 lessons

The week at a glance

One lesson a day for a week. Each day adds one idea about measuring, so run them in order.

Day	Lesson	Children learn and do	On screen
1	Lay them end to end	Measure a length by laying same-size units end to end and counting	Lay them end to end
2	The gap trap	See how gaps or overlaps spoil the count; units must touch	The gap trap
3	Same-size units	Learn that every unit must be the same size, or the count means nothing	Mixed-up units
4	Big units, small numbers	Measure the same strip in small then big units and watch the number drop	Big units, small numbers
5	Whose desk is longer?	Measure two things with the same unit and compare the counts	Whose desk is longer?

How the week builds

In Foundation, children compared two lengths by lining up one end. This week that comparison turns into a count: how many units long? The three rules of a fair count are laid out one at a time (end to end, no gaps, same size), then Day 4 shows that the unit you pick changes the number, and Day 5 uses one shared unit to compare. It opens the way to measuring with a ruler in Year 2, where the units become centimetres.

Materials for the week (one trip)

From the classroom: scissors, pencils, this pack printed.
Sets of same-size units to lay end to end: connecting cubes, wooden blocks and paperclips work well. Keep each set to one size, so a count stays fair.
The printed unit strips in this pack (cut-out sheet 1), for children without a set of cubes to hand.
A few everyday objects to measure: a pencil, a shoe, a book, a desk. No special equipment to buy.

A note homeHome practice

Dear families

This week in maths, Year 1 measures how long things are without a ruler. We lay same-size units end to end, count them, and learn the rules that keep a count fair: no gaps, no overlaps, and every unit the same size.

Try this at home

Measure a spoon or a book with same-size blocks laid end to end. How many blocks long is it?
Use pieces of dry pasta as your units. Lay them touching, with no gaps, and count.
Measure the hallway in footsteps, heel to toe. Count your steps, then count a grown-up’s.
Measure the same thing in big steps and little steps. Which gives the smaller number, and why?

My measuring this week

Fill one row a day. Tick when you laid same-size units end to end and counted them.

Day	What I measured	I used same units	How many units
Monday		□
Tuesday		□
Wednesday		□
Thursday		□
Friday		□

Printed from the free seegongsik measurement teaching pack · seegongsik.com/au/y1/measurement/AC9M1M02/pack

Day 1 · Teacher planDay 1 of 5

Lay them end to end

In Foundation, children compared two lengths by lining up one end. Today that comparison becomes a count. We lay same-size units, one after another, touching end to end, and count how many make the length. Laying them end to end is the whole idea.

We are learning to

lay same-size units end to end along an object,
start at the very end and leave no gaps,
count the units to say how long the object is.

Success criteria

I can lay units end to end from one end.
I can count them and say how many units long it is.

You need

Sets of same-size units to lay: connecting cubes, wooden blocks or paperclips, one set per pair. A few objects to measure (a pencil, a shoe, a book). The printed unit strips (cut-out sheet 1) for anyone without cubes. The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	How many blocks long? Hold a pencil beside a line of cubes. Start the first cube at the very tip of the pencil, then add another, touching. Ask: “Where does the first block go? How do we make sure we count fairly?”
20 min	Lay and count Pairs measure the objects on the worksheet, laying units from one end, touching, no gaps, then counting. Ask: “Read them aloud with me: one, two, three. Each block touches the last one.”
10 min	Say how many Children write the count for each object and check a neighbour started at the end. Ask: “How long is your pencil? Did your blocks all touch, with no gaps?”

Two short bursts instead? End the first burst after laying and counting the pencil. Start the second by measuring a longer object, like a shoe, and counting on from there.

On the board

Open the interactive unit and show “Lay them end to end”. Press “Lay the next block” and one block appears at a time, each touching the last, never overlapping. The cricket bat comes out about 7 and a bit blocks long, so the class meets “about” when the last unit does not quite fit. Press “Start again” to lay it once more.

seegongsik.com/au/y1/measurement/AC9M1M02

Watch for these ideas

Starting the first unit part way along, not at the very end, so the count comes out wrong.
Counting the gaps between units, or the lines, instead of the units themselves.
Thinking bigger, brighter objects need bigger numbers no matter the unit.

Answers

Pencil = 6 cubes, marker = 4 cubes, glue stick = 5 cubes. The unit boxes are printed under each object, so a correct count matches the boxes.
A fair count starts at the very end, with units touching end to end and no gaps.
Draw-your-own varies: check the units are the same size and drawn touching.

Day 1 · Worksheet

Lay them end to end

NameClassDate

Each object has unit boxes under it. Count the boxes from one end to the other. Then write how many cubes long it is.

a pencil

This is ______ cubes long.

a marker

This is ______ cubes long.

a glue stick

This is ______ cubes long.

Measure your own

Find a real object. Lay same-size cubes end to end along it and count. Then draw your cubes.

Draw the object and your cubes touching, end to end

My object is ______ cubes long.

Day 2 · Teacher planDay 2 of 5

The gap trap

A count is only fair when the units touch. Today children meet the trap: leave gaps and the count comes out too small, overlap the units and it comes out too big. The rule is simple, end to end, no gaps, no overlaps.

We are learning to

lay units so they touch, with no gaps and no overlaps,
spot a measurement that used gaps or overlaps,
say why gaps make the count too small and overlaps make it too big.

Success criteria

I can tell a fair measurement from one with gaps.
I can give the true count and say why the other is wrong.

You need

Same-size units (cubes or blocks). A ribbon or strip of paper to measure. The worksheet, one per child. It helps to have one child lay units with gaps on purpose, so the class can see the trap.

Lesson flow (about 40 minutes)

10 min	Two counts, one ribbon Measure a ribbon fairly and get 8. Then measure it again with gaps and get only 6. Ask: “Same ribbon, same blocks. Why did the number change? Where did the length go?”
20 min	Spot the fair one Children look at the two measurements on the worksheet, circle the fair one and write the true count. Then they lay their own units to check. Ask: “Which row has no gaps? That is the fair count. What is the true number?”
10 min	Say the rule Children finish the sentence: units must touch because. Overlaps get a mention too. Ask: “Gaps make the count too small. What do overlaps do to the count?”

Two short bursts instead? End the first burst after spotting the fair one. Start the second by making an overlap on purpose and counting the units twice.

On the board

Show “The gap trap”. Press “No gaps (fair)” and place the blocks: six, the true count. Press “With gaps” and only five fit, too few, because the gaps quietly steal length. Press “Overlapping” and seven fit, too many, because overlaps measure the same length twice. Let the class call each number.

seegongsik.com/au/y1/measurement/AC9M1M02

Watch for these ideas

Leaving small gaps between units and still trusting the count.
Overlapping units so the same bit of length is counted twice.
Thinking any row of blocks gives the right answer, however it is laid.

Answers

Row A (units touching) is the fair measurement. The ribbon is 8 cubes long.
Row B has gaps, so only 6 units fit; gaps make the count too small.
Units must touch because gaps leave length uncounted and overlaps count length twice.

Day 2 · Worksheet

The gap trap

NameClassDate

Two children measured the same ribbon with the same cubes. Circle the one who measured fairly. Then write the true length.

Row A

Cubes touch, end to end.

Row B

Cubes have gaps between them.

The fair measurement

The fair one is Row ______. The ribbon is ______ cubes long.

Say how you know

Gaps make the count wrong because ____________________

Day 3 · Teacher planDay 3 of 5

Same-size units

Yesterday the rule was: no gaps. Today it is the other half: every unit must be the same size. Mix a big block with a small one and the count still gives a number, but it no longer means a length. Six of what, exactly?

We are learning to

measure using units that are all the same size,
see why mixing big and small units breaks the count,
say that a count only means a length when the units are uniform.

Success criteria

I can choose units that are all the same size.
I can say why a count with mixed units means nothing.

You need

A set of same-size units and a few odd ones of a different size (a big block among the small cubes). A book or strip to measure. The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Six of what? Measure a book with 8 equal cubes. Then measure it again with big and small blocks mixed and get 6. Ask: “Both times we got a number. But six of what? Can we trust it?”
20 min	Sort and measure Children pick a set of same-size units, measure the book on the worksheet and write the uniform count. Then they look at the mixed row and say why it fails. Ask: “What did you do first to make your count fair? Why toss out the odd-size block?”
10 min	Say the rule Children finish: units must all be the same size because. Ask: “If my friend used bigger cubes than you, could we compare our counts?”

Two short bursts instead? End the first burst after measuring with same-size cubes. Start the second by comparing two children who used different-size cubes.

On the board

Show “Mixed-up units”. Press “All the same” and count the beach towel: eight equal blocks, so the number 8 actually means something. Press “Big and small mixed” and count again: six, but six of what? With big and small mixed, the count stops meaning anything. Let the class explain the difference.

seegongsik.com/au/y1/measurement/AC9M1M02

Watch for these ideas

Mixing a big block in with small ones and still reading off the count.
Thinking any objects can be units, even when they are different sizes.
Comparing two counts taken with different-size units as if they matched.

Answers

Row A (all the same size) is the fair measurement. The book is 8 cubes long.
Row B mixes big and small units, so its count of 6 does not tell a length.
Units must be the same size because only then does each one add the same amount to the count.

Day 3 · Worksheet

Same-size units

NameClassDate

The same book was measured two ways. Circle the row that used same-size units. Then write how long the book is.

Row A

All the units are the same size.

Row B

Big and small units are mixed together.

The fair measurement

The fair one is Row ______. The book is ______ cubes long.

Say how you know

Units must all be the same size because ____________________

Day 4 · Teacher planDay 4 of 5

Big units, small numbers

Here is the surprise of the week: measure the same strip with a bigger unit and the number gets smaller. Fewer big steps fit than small steps. So a bigger number does not always mean a longer thing, it depends on the unit.

We are learning to

measure the same length with a small unit, then a big one,
notice the count goes down when the unit gets bigger,
say that a bigger number does not always mean a longer thing.

Success criteria

I can measure one strip in small units and in big units.
I can say which unit gives the smaller number and why.

You need

Two sizes of unit, where the big one is about twice the small one (small cubes and long blocks, or paperclips and lolly sticks). A strip of card to measure. The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Same strip, two units Measure a strip with small cubes: 8. Then measure the very same strip with big blocks: 4. Ask: “The strip did not change. Why did the number get smaller?”
20 min	Count both ways Children measure the strip on the worksheet in small units, then big units, and write both counts. Ask: “Which unit needed more of them to cover the strip? Which gave the bigger number?”
10 min	Bigger number, longer? Children decide if a bigger number always means a longer thing, and give a reason. Ask: “Ten paperclips or three blocks. Which is longer? What must you ask first?”

Two short bursts instead? End the first burst after counting in small units. Start the second by counting the same strip in big units and comparing.

On the board

Show “Big units, small numbers”. Press “Thongs”, “Crayons” and “Paperclips” in turn to measure one surfboard three ways: 4 thongs = 8 crayons = 16 paperclips. The board never changed, so the bigger the unit, the smaller the number, every time. Let the class predict before you press.

seegongsik.com/au/y1/measurement/AC9M1M02

Watch for these ideas

Thinking the bigger number always means the longer thing, without asking about the unit.
Expecting the count to stay the same when the unit changes.
Guessing that a bigger unit needs a bigger number, not a smaller one.

Answers

Small units: 8. Big units: 4. The same strip, so 8 small = 4 big.
The big unit gives the smaller number, because each big unit covers more of the strip, so fewer are needed.
A bigger number does not always mean longer: you must know the size of the unit first.

Day 4 · Worksheet

Big units, small numbers

NameClassDate

Here is one strip, measured two ways. Count the small units, then the big units. Write both counts.

Small units

The strip is ______ small units long.

Big units

The same strip is ______ big units long.

What changed?

The ______ unit gives the smaller number.

A bigger number does not always mean longer because ____________________

Day 5 · Teacher planDay 5 of 5

Whose desk is longer?

The week comes together today. To compare two things fairly, measure them both with the same unit, then compare the counts. If the units differ, the numbers cannot be trusted. The bigger count is longer, and the difference tells you by how many units.

We are learning to

measure two objects with the same unit,
compare the counts to say which is longer,
say by how many units longer, using the difference.

Success criteria

I can measure two things with the same unit.
I can say which is longer and by how many units.

You need

One set of same-size units for the whole comparison (do not mix sizes). Two objects to compare, like two desks or two ribbons. The worksheet, one per child. The mini-check to hand out at the end.

Lesson flow (about 40 minutes)

10 min	Same unit for both Measure two desks, first with different hands, then with the same blocks. Ask: “Different hands gave a muddle. Why does one shared unit let us compare fairly?”
20 min	Measure, compare, subtract Pairs measure two ribbons on the worksheet in the same cubes, say which is longer, and work out by how many. Then the mini-check. Ask: “Ben’s is 12, Ava’s is 9. Which is longer? How many more cubes is that?”
10 min	Mini-check Hand out the mini-check at the back of the pack. Children work on their own; read each question aloud for those who need it.

Two short bursts instead? End the first burst after measuring and comparing the two ribbons. Start the second with the mini-check on its own.

On the board

Show “Whose desk is longer?”. Press “Next step”: Mia counts 8 of her small hands and Tom counts 7 of his big hands, so the counts cannot compare. Press again and both desks are measured with the same blocks, Mia 10 and Tom 11, so Tom’s desk is longer by one block. Press “Start again” to replay the trap.

seegongsik.com/au/y1/measurement/AC9M1M02

Watch for these ideas

Comparing two counts that were taken with different-size units, as if the numbers matched.
Saying which is longer but not working out by how many.
Forgetting to lay units end to end, with no gaps, on the second object too.

Answers

Ava’s ribbon = 9 cubes, Ben’s ribbon = 12 cubes.
Ben’s is longer. It is 12 - 9 = 3 cubes longer.
Measure-your-own varies: check both objects were measured with the same unit, and the difference matches the two counts.

Day 5 · Worksheet

Whose is longer?

NameClassDate

Both ribbons were measured with the same cubes. Count each one. Then say which is longer and by how many cubes.

Ava's ribbon

This is ______ cubes long.

Ben's ribbon

This is ______ cubes long.

Compare

______’s ribbon is longer. It is ______ cubes longer than the other one.

Measure your own

Find two things in the room. Measure both with the same cubes. Draw them and count.

Draw both things and your cubes, end to end, no gaps

The ______ is longer by ______ cubes.

Cut-out cards 1 of 2Unit strips

Same-size unit strips

Cut along the dashed lines to make a set of same-size units. Keep each strip in its own pile, so every unit in a pile is the same size. Lay them end to end, touching, with no gaps, to measure. Use them all week.

Cube units

Paperclip units

Teacher note: the cube units are all one size and the paperclip units are all another. Do not mix the two piles in one measurement, or the count stops meaning a length (Day 3).

Cut-out cards 2 of 2Objects to measure

Things to measure

Measure each object with your cube units. Lay them from one end, touching, with no gaps, then count. Write how many cubes long it is.

a crayon

It is ______ cubes long.

a pencil

It is ______ cubes long.

a book

It is ______ cubes long.

a shoe

It is ______ cubes long.

Teacher note (cube counts): crayon = 3, pencil = 6, book = 8, shoe = 9. Each object is printed exactly that many cube units long, so a fair measurement matches. The cube strip on sheet 1 is the matching unit.

Mini-check · End of the weekMeasure with units

What we know: measuring with informal units

NameClassDate

Work on your own. Your teacher can read the questions to you. Say how you know when you can.

Count the cubes. How many cubes long is this pencil?
a pencil
It is ______ cubes long.
Which measurement is right: the one with gaps between the units, or the one laid end to end with no gaps? Circle it.
Why must all the units be the same size? ____________________
You measure one strip with big blocks and with small cubes. Which unit gives the smaller number, the big one or the small one? Circle it.
These two ribbons were measured with the same cubes. Which is longer, and by how many cubes?
Ribbon 1
Ribbon 2
Ribbon ______ is longer, by ______ cubes.

Mini-check · Answers and markingFor the teacher

Answers and marking guide

Answers

7 cubes (the seven printed units, end to end).
The one laid end to end, with no gaps.
So each unit adds the same amount, and the count means a real length. Mixed sizes make the count meaningless.
The big unit gives the smaller number (fewer big units fit the same strip).
Ribbon 2 is longer, by 3 cubes (9 - 6 = 3).

A quick three-level guide

Idea	Working towards	At standard	Beyond
End to end (Q1)	guesses a number	lays units end to end and counts	starts at the very end and checks the last unit
No gaps (Q2)	trusts any row of units	picks the row laid end to end	explains gaps make the count too small
Same size (Q3)	mixes unit sizes	measures with same-size units	explains why uniform units let a count mean a length
Unit and number (Q4)	thinks bigger unit gives a bigger number	knows the bigger unit gives the smaller number	explains fewer big units fit the same length
Compare (Q5)	compares counts from different units	measures both with one unit and compares	gives the difference: longer by how many units

Five questions, five ideas. A child at standard lays same-size units end to end, counts them, and compares two things with one unit.

Weekly recordClass checklist

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	End to end	No gaps	Same size	Big unit, small number	Compare two things

The five columns are the five days: lay units end to end, no gaps, same-size units, a bigger unit gives a smaller number, and comparing two things with one unit.