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This guide explains each lesson in easy English. It gives you the ideas, the words, the questions and the games. Read a topic the night before. Then teach it to Lia in your own way.

Lia can count to 100. The new part is the number line: reading a number from its place on the line, and estimating when there is no number. A good estimate is close. It does not have to be exact.

Made by Lia's dad with the help of AI. It follows the order of the White Rose Maths Year 2 small steps (Autumn Block 1, steps 9–11). It is home practice, not official school or White Rose material. If the school teaches something in a different way, follow the school.

Goes with “Lia's Maths Book”. →

What is in this guide

How to use this guide

Every topic has the same parts. Here is what they mean.

Part	What it is for
The big idea	The one thing Lia must understand. Read this first.
Get ready	Things to put on the table before you start: a strip of paper, a ruler, a pencil.
Teach it, step by step	A small lesson in 3–5 steps. You lines are things you can say. Lia lines are answers she might give. Do lines tell you what to do with your hands.
Other ways to say it	The same question in different English. Lia will hear all of them at school.
Worksheet English	Instructions that are often printed on maths worksheets. Read them together.
Good questions to ask	Questions that make Lia think and explain.
If Lia is stuck	Common mistakes and what to say.
Game	A short game on the floor or on a strip of paper.

The big ideaWhat it is forThe one thing Lia must understand. Read this first.
Get readyWhat it is forThings to put on the table before you start: a strip of paper, a ruler, a pencil.
Teach it, step by stepWhat it is forA small lesson in 3–5 steps. You lines are things you can say. Lia lines are answers she might give. Do lines tell you what to do with your hands.
Other ways to say itWhat it is forThe same question in different English. Lia will hear all of them at school.
Worksheet EnglishWhat it is forInstructions that are often printed on maths worksheets. Read them together.
Good questions to askWhat it is forQuestions that make Lia think and explain.
If Lia is stuckWhat it is forCommon mistakes and what to say.
GameWhat it is forA short game on the floor or on a strip of paper.

A good maths time at home (15–20 minutes)

Time	What to do
2 minutes	Warm up. Play one quick game from this guide.
5 minutes	Teach the big idea with a paper number line or a tape line on the floor. Use the “Teach it” steps.
8–10 minutes	Workbook. One Part is enough. Sit next to Lia. Ask her to explain each answer.
2 minutes	Talk. “What did you learn today? What was tricky?”

2 minutesWhat to doWarm up. Play one quick game from this guide.
5 minutesWhat to doTeach the big idea with a paper number line or a tape line on the floor. Use the “Teach it” steps.
8–10 minutesWhat to doWorkbook. One Part is enough. Sit next to Lia. Ask her to explain each answer.
2 minutesWhat to doTalk. “What did you learn today? What was tricky?”

About languages

If Lia does not understand an English word, you can explain it quickly in Korean. Then say the English word again, and ask her to say it too. Always finish in English.

On one page

Put this on the fridge.

Part	Topic	The big idea in one line	Key words	Workbook
Part 1	10s on a number line	Count in 10s along the line. Each interval is worth 10.	number line, interval, label	10s on the line
Part 2	10s and 1s on a number line	47 is between 40 and 50. Start at the nearest 10, not at 0.	between, closer to, count on	10s and 1s
Part 3	What is each step worth?	Count the intervals between two numbers. A step can be 1, 2, 5 or 10.	interval, worth	What is each step worth?
Part 4–6	Estimate on a number line	Find halfway. Which end is closer? A good estimate is close.	estimate, about, halfway	Estimate the arrow, Mark the number, Think about it

Part 1Topic10s on a number lineThe big idea in one lineCount in 10s along the line. Each interval is worth 10.Key wordsnumber line, interval, labelWorkbook10s on the line
Part 2Topic10s and 1s on a number lineThe big idea in one line47 is between 40 and 50. Start at the nearest 10, not at 0.Key wordsbetween, closer to, count onWorkbook10s and 1s
Part 3TopicWhat is each step worth?The big idea in one lineCount the intervals between two numbers. A step can be 1, 2, 5 or 10.Key wordsinterval, worthWorkbookWhat is each step worth?
Part 4–6TopicEstimate on a number lineThe big idea in one lineFind halfway. Which end is closer? A good estimate is close.Key wordsestimate, about, halfwayWorkbookEstimate the arrow, Mark the number, Think about it

Every day, ask these three questions

Question 1
“What is each interval worth?”
Question 2
“Where is halfway?”
Question 3
“Explain how you know.”

Next in class

After these steps, the class will compare and order numbers. The number line helps there too: the number further to the right is greater. Later, the same idea comes back when Lia reads rulers and scales, and in Year 3 on number lines up to 1,000.

Next: Compare and order numbers →

Teaching Guide · Number lines and estimating · liabooks.com/study

Background A

How maths is taught in Year 2영국 Year 2 수학 수업 방식

What happens in Lia's classroom, so you can teach in the same way at home.

Small steps

Lia's school uses a plan called White Rose Maths. Each unit is cut into many small steps. The Addition and Subtraction unit has 21 small steps. This guide covers the first six. Each step is one small idea, and each new step uses the step before it. That is why the early steps, like bonds to 10, are so important.

Objects → pictures → numbers

Teachers call this concrete → pictorial → abstract. It means:

Stage	What it means	Example: 7 + 3
Concrete	Real things you can touch and move.	7 red Lego bricks and 3 blue Lego bricks. Count them all: 10.
Pictorial	A drawing of the things.	A ten frame with 7 dots and 3 dots.
Abstract	Only numbers and signs.	7 + 3 = 10

ConcreteWhat it meansReal things you can touch and move.Example: 7 + 37 red Lego bricks and 3 blue Lego bricks. Count them all: 10.
PictorialWhat it meansA drawing of the things.Example: 7 + 3A ten frame with 7 dots and 3 dots.
AbstractWhat it meansOnly numbers and signs.Example: 7 + 37 + 3 = 10

Children do not always move in one direction. A child who is stuck on numbers goes back to pictures or objects. This is normal and good.

Three kinds of question

Kind	What it asks	Example
Fluency	Can you do it quickly and correctly?	“What is 6 + 4?”
Reasoning	Can you explain why? Is it true or false?	“Max says 20 + 50 = 700. Is he right? How do you know?”
Problem solving	Can you use it in a new or tricky situation?	“Find two numbers that make 10. Now find all of them.”

FluencyWhat it asksCan you do it quickly and correctly?Example“What is 6 + 4?”
ReasoningWhat it asksCan you explain why? Is it true or false?Example“Max says 20 + 50 = 700. Is he right? How do you know?”
Problem solvingWhat it asksCan you use it in a new or tricky situation?Example“Find two numbers that make 10. Now find all of them.”

Many children in Korea are very strong at fluency. The school will also ask Lia to reason and explain in English. This is where you can help the most.

Full sentences

Teachers give children sentence stems. A sentence stem is the start of a sentence with gaps. Children fill the gaps and say the whole sentence. For example:

“The whole is ___. The parts are ___ and ___.”
“I know ___, so I know ___.”
“___ and ___ make 10.”

At home, when Lia gives a one-word answer, you can say: “Can you say it in a full sentence?” Then help her with a stem from this guide.

Words the school uses

The school says	Not	Why it matters
maths	math	British English. Lia's school is British.
ones and tens	units	White Rose says “ones”. Older books say “units”.
number sentence	equation (in Year 2)	“4 + 6 = 10” is a number sentence.
take away, subtract, minus	—	All three mean −. Children hear all three.
equals, is equal to, is the same as	—	The = sign means both sides have the same value.

mathsNotmathWhy it mattersBritish English. Lia's school is British.
ones and tensNotunitsWhy it mattersWhite Rose says “ones”. Older books say “units”.
number sentenceNotequation (in Year 2)Why it matters“4 + 6 = 10” is a number sentence.
take away, subtract, minusNot—Why it mattersAll three mean −. Children hear all three.
equals, is equal to, is the same asNot—Why it mattersThe = sign means both sides have the same value.

Teaching Guide · Number lines and estimating · liabooks.com/study

Background B

The five pictures (models)다섯 가지 그림 모델

Lia will see these pictures in class. Learn them once. You will use them all year.

A model is a picture that shows a maths idea. Models help children see the maths. Each model below has: what it is, how to make it at home, and what to say.

1. Ten frame

7 green and 3 red. 7 and 3 make 10.

What it is: A box with 10 spaces, in 2 rows of 5. It shows how many there are, and how many more make 10.

Make it at home: Cut 2 cups off an egg box of 12, so it has 10 cups. Or draw a 2 × 5 grid on paper. Use coins, beads or small toys as counters.

YOU“How many counters can you see?”

YOU“How many empty spaces are there?”

YOU“So how many more do we need to make 10?”

YOU“Look at the top row. It has 5. The top row is full, so we know there are at least 5.”

2. Part–whole model

The whole is 13. The parts are 9 and 4.

What it is: One big circle at the top (the whole) and two circles under it (the parts). The parts together make the whole.

Make it at home: Draw three circles on paper. Put real counters in them.

YOU“This is the whole. The whole is 13.”

YOU“These are the parts. The parts are 9 and 4.”

YOU“9 and 4 make 13.”

YOU“If we take away one part from the whole, the other part is left.”

3. Bar model

The whole is 16. One part is 9. What is the other part?

What it is: The part–whole idea drawn as long bars. The top bar is the whole. The bottom bars are the parts. It is very useful for story problems, because it shows what we know and what we need to find.

Make it at home: Cut strips of paper. Or draw rectangles. Write a question mark on the part you need to find.

YOU“The top bar is the whole. It is 16.”

YOU“This part is 9. This part is a mystery. What is it?”

YOU“9 plus what equals 16? Or: 16 take away 9 is what?”

4. Tens and ones (base 10)

3 tens and 4 ones = 34

What it is: A long stick is 1 ten (10 small cubes stuck together). A small cube is 1 one. The picture shows 3 tens and 4 ones, so the number is 34.

Make it at home: Make towers of 10 Lego bricks. Each tower is a ten. Single bricks are ones. Or tie 10 straws or 10 ice-cream sticks with a rubber band. You can also use money: ten 10 sen coins make RM1.

YOU“How many tens are there? How many ones?”

YOU“3 tens and 4 ones. That is 34.”

YOU“The 3 in 34 means 3 tens. It is worth 30.”

YOU“The 4 in 34 means 4 ones. It is worth 4.”

5. Number line

8 + 5: jump 2 to get to 10, then jump 3 more. You land on 13.

What it is: A line with numbers in order. Adding means jumping forward (to the right). Subtracting means jumping back (to the left).

Make it at home: Use a ruler or a tape measure. Or write 0 to 20 on sticky notes on the floor, and let Lia jump on them.

YOU“Put your finger on 8.”

YOU“Jump forward 2. Where are you now?”

LIA10!

YOU“Good. Now jump forward 3 more. Where are you?”

LIA13.

YOU“So 8 add 5 is 13.”

One more picture

Lia may also see a rekenrek in class. It is a bead frame with two rows of 10 beads. The beads change colour after 5, so children can see 5 and 10 at a glance. It shows the same ideas as the ten frame.

Add by making 10 (with the rekenrek) →

Teaching Guide · Number lines and estimating · liabooks.com/study

Part 1 · Step 9 · Workbook pages 2

10s on a number line수직선에서 10씩 세기

Count in 10s along the line. Each interval is worth 10.

한국어 요약

0–100 수직선을 10씩 세어 읽는 법을 영어로 가르쳐요. 양끝에만 숫자가 있을 때 10의 배수를 채우는 법, 화살표가 가리키는 10의 배수를 읽는 법, 눈금 한 칸을 1로 세는 실수를 바로잡는 대본과 놀이를 담았어요.

The big idea핵심

A number line shows numbers in order. Small numbers are on the left. Big numbers are on the right.

This line goes from 0 to 100. It has 10 intervals (the gaps between the marks). Each interval is worth 10, so we count in 10s: 0, 10, 20, 30 … 100.

When only the ends have numbers, count in 10s from the nearest number you know.

Count in 10s: 0, 10, 20 … 100

10, 20, 30, 40, 50. Arrow A points to 50.

Get ready준비물

A long strip of paper (about 1 metre) and a pen
10 Lego towers of 10 bricks, all the same length
Sticky notes

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Make a 10s line

DODraw a long line on the paper. Write 0 at the left end and 100 at the right end.

DOLay the 10 towers along the line, end to end. Draw a mark where each tower ends.

YOU“How many towers are there? How much is each tower worth?”

LIA10 towers. Each one is 10.

YOU“Let's count in 10s along the line. 10, 20, 30 …”

LIA… 80, 90, 100!

Find the missing numbers

DOWrite all the 10s on the line. Then cover some of them with sticky notes. Leave 0 and 100.

YOU“What number is under this sticky note?”

LIA70.

YOU“How do you know?”

LIAI counted in 10s from 0. 10, 20 … 70.

YOU“And this one, next to 100?”

LIA90. It is 10 less than 100.

Counting back from the nearer end is quicker. Praise it when Lia does it.

Where is the arrow?

DODraw an arrow above the third mark from 0.

YOU“What number is the arrow pointing to?”

LIA3?

YOU“Each interval is worth 10, not 1. Count the jumps in 10s.”

LIA10, 20, 30. It is 30!

Many children count the marks as 1, 2, 3. Before every number line, ask: “What is each interval worth?”

Other ways to say it다른 표현

“What number is the arrow pointing to?”
“Which number goes here?”
“What number is missing?”
“Count in 10s along the line.”
“How many 10s is that?”
“Count back from 100.”

Worksheet English표현

“Label the number line.”
“Complete the number line.”
“What number is the arrow pointing to?”

Good questions to ask좋은 질문

“How many intervals are there from 0 to 100?”
Note
10. Each one is worth 10.
“Where did you start counting? Why?”
Good answers
“From 0.” / “From 100. I counted back because it was closer.”
“Is the arrow nearer to 0 or to 100?”
Note
This helps her check that the answer makes sense.

If Lia is stuck막힐 때

When
Lia reads the arrow on the third mark as “3”.
“What is each interval worth?” Lay a tower of 10 on each interval and count the towers in 10s.
When
She writes 1, 2, 3 in the boxes.
“Look at the ends. 0 and 100. Can we get to 100 in 1s with only 10 jumps?” Count in 10s together.
When
She counts from 0 every time, even next to 100.
Point at the nearest number with a label. “Start here. Count back in 10s from 100.”

Game놀이

Game · Floor number line

You need: masking tape on the floor, 11 paper cards with 0, 10, 20 … 100

Tape a long line on the floor. Put 0 at one end and 100 at the other end.
Lia puts the cards 10, 20 … 90 in the right places. Then she walks along the line and counts in 10s.
Call a number: “70!” Lia jumps to it. Then swap: Lia calls a number and you jump.

In the workbook

Fill in the 10s on number lines, and read where the arrows point.

Teaching Guide · Number lines and estimating · liabooks.com/study

Part 2 · Step 10 · Workbook pages 3

10s and 1s on a number line수직선에서 10과 1로 읽기

Find the nearest 10 first. Then count on or back in 1s.

한국어 요약

두 10 사이에 있는 수를 수직선에서 읽고 놓는 법을 영어로 가르쳐요. 47은 40과 50 사이에 있고 50에 더 가깝다는 생각, 40–50처럼 짧은 선은 시작 수부터 읽는 법, 0부터가 아니라 가까운 10에서 세는 법을 담았어요.

The big idea핵심

Every number lives between two 10s. 47 is between 40 and 50. It is 7 more than 40 and 3 less than 50, so it is closer to 50.

To find a number, go to the nearest 10 first. Then count on (or back) in 1s. Do not start from 0.

Some lines are short, like 40 to 50. Read the first number first. A number line does not always start at 0.

A is 47: start at 40, then 41, 42 … 47

47 is between 40 and 50

Get ready준비물

The paper number line from Part 1
A ruler with centimetres (a ruler is a number line too)
Lego towers of 10 and single bricks

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Between two 10s

DOBuild 47: 4 towers of 10 and 7 single bricks.

YOU“Which two 10s is 47 between?”

LIA40 and 50.

YOU“Is it closer to 40 or to 50?”

LIA50. Only 3 more bricks make another 10.

Start at the nearest 10

DOPoint to 80 on the paper line.

YOU“Find 82. Do we start from 0?”

LIANo. Start at 80. 81, 82.

YOU“Now find 89. Which 10 is closer, 80 or 90?”

LIA90. Count back 1: 89.

Counting from the nearest 10 is fast. Counting from 0 is slow and easy to get wrong.

A short line

DODraw a short line. Write 40 at the start and 50 at the end. Draw 9 small marks in between.

DODraw an arrow above the sixth mark.

YOU“What number is the arrow pointing to?”

LIA6?

YOU“Look at the start of the line. What number is it?”

LIA40. Oh, so it is 46!

Ask Lia to read the first number out loud before she counts. Do this on every short line.

Put it on the line

YOU“Draw an arrow to show where 74 goes.”

LIAIt is between 70 and 80. Start at 70: 71, 72, 73, 74. Here.

YOU“Is 74 closer to 70 or to 80?”

LIACloser to 70.

Other ways to say it다른 표현

“Which two 10s is it between?”
“Is it closer to 40 or to 50?”
“Start at the nearest 10.”
“Count on in 1s.”
“Count back from 50.”
“What number does the line start at?”

Worksheet English표현

“Complete the number line.”
“What number is the arrow pointing to?”
“Draw an arrow to show where 74 goes.”
“Mark 38 on the number line.”

Good questions to ask좋은 질문

“Which two 10s is 37 between?”
Good answers
“30 and 40. It is closer to 40.”
“Did you start from 0? Is there a quicker way?”
Good answers
“I started at 80 because it was the nearest 10.”
“What number does this line start at?”
Note
Ask it before every short line.

If Lia is stuck막힐 때

When
Lia counts every mark from 0, one by one.
Cover the start of the line with your hand. “Find the nearest 10 first. Then count on in 1s.”
When
On a line from 40 to 50, she reads the arrow as “6”.
“Read the first number first. What is it?” Then count on together from 40: 41, 42 … 46.
When
She puts 89 just after 80.
“Is 89 closer to 80 or to 90?” Show it with bricks: 89 needs only 1 more to make 90.

Game놀이

Game · Big step, small steps

You need: the floor number line from Part 1

Call a number, like 53. Lia jumps to the nearest 10 first (50). Then she takes small steps: 51, 52, 53.
Before she moves, she says which 10 is closer: “53 is closer to 50.”
Swap. Lia calls a number for you. Make a mistake on purpose. Can she catch it?

In the workbook

Short lines in 1s to fill in, arrows to read on longer lines, and two numbers to place exactly.

Teaching Guide · Number lines and estimating · liabooks.com/study

Part 3 · Step 10 · Workbook pages 4

What is each step worth?눈금 한 칸의 값 찾기

Count the intervals between two numbers. Then count in that step.

한국어 요약

눈금마다 숫자가 없을 때 한 칸의 값(1, 2, 5, 10)을 찾는 법을 영어로 가르쳐요. 숫자가 있는 두 눈금 사이를 몇 칸으로 나눴는지 세고 그 값으로 뛰어 세는 대본을 담았어요. 길이·무게 단원의 눈금 읽기와 같은 생각이에요.

The big idea핵심

Not every interval is worth 1. It can be worth 1, 2, 5 or 10. Before you read a number line, ask: “What is each interval worth?”

Find two marks that have numbers. Count the intervals between them. 0 to 10 in 5 intervals → each one is worth 2. 0 to 10 in 2 intervals → each one is worth 5.

Then count in that step: 2, 4, 6 … or 5, 10, 15 …

5 intervals from 0 to 10. Each one is worth 2.

2 intervals from 10 to 20. Each one is worth 5.

Get ready준비물

Paper and a pencil
A ruler, or a kitchen scale or jug with marks on it, if you have one
Counters or small toys to jump along the line

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Count the intervals

DODraw a line from 0 to 10 with 4 marks in between. That makes 5 intervals.

YOU“How many intervals are there from 0 to 10?”

LIA5.

YOU“5 jumps make 10. So each jump is worth …?”

LIA2! 2, 4, 6, 8, 10.

Count the intervals (the gaps), not the marks. This line has 6 marks but only 5 intervals.

Same numbers, different steps

DODraw another line from 0 to 10, with only one mark in the middle.

YOU“How many intervals now?”

LIA2. So each one is 5.

YOU“The numbers at the ends are the same. Only the intervals are different.”

Read the arrow

DODraw a line from 50 to 100. Write 50, 60, 70, 80, 90 and 100. Add one mark between each pair. Draw an arrow above the mark between 80 and 90.

YOU“What is each interval worth?”

LIA5. There are 2 jumps from 80 to 90.

YOU“So the arrow is pointing to …?”

LIA85.

Other ways to say it다른 표현

“What is each interval worth?”
“What is each jump worth?”
“How many intervals are there between 0 and 10?”
“What are we counting in?”
“Are we counting in 2s, 5s or 10s?”

Worksheet English표현

“What is each interval worth?”
“Complete the number line.”
“What number is the arrow pointing to?”

Good questions to ask좋은 질문

“How did you work out the interval?”
Good answers
“There are 5 jumps from 0 to 10. 5 jumps of 2 make 10.”
“What would this line look like if each interval was worth 1?”
Note
It would have 10 intervals from 0 to 10.
“Where else do we see lines like this?”
Note
Rulers, kitchen scales, jugs and thermometers all have marks like this.

If Lia is stuck막힐 때

When
Lia counts each interval as 1.
“Look at the two numbers, 0 and 10. How many jumps? Can 5 jumps of 1 get to 10?”
When
She counts the marks, not the intervals.
Put a counter on 0. Jump it to each mark and count the jumps, not the marks.
When
She counts every mark from 0 again for each arrow.
Start at the nearest number with a label, then count in the step from there: “80, 85.”

Coming later

Rulers, scales and thermometers work in the same way. When Lia reads a scale in the Year 2 length, mass and temperature lessons, she will ask the same question: “What is each interval worth?”

Game놀이

Game · Guess my step

You need: paper and a pencil

Draw a line. Write a number at each end and draw the marks. Do not say what the step is.
Lia says what each interval is worth and writes one missing number.
Swap. Lia draws a line for you. Try steps of 2, 5 and 10.

In the workbook

Number lines in 2s, 5s and 10s: fill in the boxes, say what each interval is worth, and read the arrows.

Teaching Guide · Number lines and estimating · liabooks.com/study

Part 4–6 · Step 11 · Workbook pages 5–7

Estimate on a number line수직선에서 어림하기

Find halfway. Which end is closer? A good estimate is close.

한국어 요약

눈금에 숫자가 없을 때 화살표가 가리키는 수를 어림하고, 수가 놓일 자리를 표시하는 법을 영어로 가르쳐요. 가운데 찾기, 더 가까운 끝 고르기, 머릿속으로 10칸 나누기, 기준점에서 확인하기의 네 단계를 대본과 놀이로 담았어요.

The big idea핵심

To estimate is to find a number that is close. A good estimate is close. It does not have to be exact.

Use four steps. 1. Find halfway. 2. Is it closer to the start, to halfway or to the end? 3. Split the line into 10 parts in your head. 4. Check from the nearest number you know.

It works both ways. Read an arrow and say the number. Or take a number and draw an arrow where it goes.

A is more than halfway. It is about 70.

10 is much less than halfway. It goes close to 0.

Get ready준비물

The floor line or paper line from Part 1, with only 0 and 100 written on it
A small toy to use as a marker
The 10s cards from Part 1, to check

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Find halfway

DOShow a line with only 0 and 100 on it.

YOU“Where is halfway? Put your finger on it.”

LIAHere, in the middle.

YOU“What number is halfway between 0 and 100?”

LIA50.

Which end is closer?

DODraw an arrow a little past 70.

YOU“Is the arrow closer to 0 or to 100?”

LIATo 100. It is more than halfway.

YOU“So is the number more than 50 or less than 50?”

LIAMore. Maybe 60 or 70.

Split it in your head

YOU“Imagine 10 jumps of 10 from 0 to 100. Where would 60 and 70 be?”

DOLet Lia point to where 60 and 70 would be.

LIAThe arrow is near 70. It is about 70.

YOU“Great estimate. A good estimate is close. It does not have to be exact.”

Accept any answer that is close, like 67 or 73. Praise the steps she used, not only the number.

Now mark a number

YOU“Where does 10 go? Is 10 more or less than halfway?”

LIALess. Much less.

YOU“So is it close to 0, or close to 50?”

LIAClose to 0. Here.

DOLet Lia put the toy there. Then check with the 10s cards from Part 1.

Many young children put 10 near the middle of a 0–100 line. Asking about halfway is the quickest fix.

Check from a number you know

YOU“Mark 46.”

LIAIt is a bit less than halfway. Just before 50.

YOU“Check from 50. How far is 46 from 50?”

LIAOnly 4. So it is very close to halfway.

Other ways to say it다른 표현

“Is it closer to 0 or to 100?”
“Where is halfway?”
“Is it more or less than halfway?”
“It is about 70.”
“It is a bit more than halfway.”
“It is a bit less than halfway.”
“Roughly where does 30 go?”

Worksheet English표현

“Estimate the number the arrow is pointing to.”
“Draw an arrow to show where 28 goes.”
“Mark 85 on the number line.”
“Explain how you know.”

Good questions to ask좋은 질문

“Explain how you know.”
Good answers
“It is a bit more than halfway, so it is more than 50. It is near 60.”
“Is your estimate sensible?”
Note
If the arrow is near 100, an answer like 20 is not sensible.
“Is 10 more or less than halfway?”
Good answers
“Less. 10 is much less than 50, so it goes close to 0.”
“Can a different number also be a good estimate?”
Note
Yes. 67, 70 and 73 can all be good estimates for the same arrow.

If Lia is stuck막힐 때

When
On a 0 to 100 line, Lia puts 10 near the middle.
“Where is halfway? Is 10 more or less than halfway?” Then: “Is 10 close to 0, or close to 50?”
When
She is upset because her estimate is not exactly right.
“An estimate only needs to be close. 67 is a great estimate for 70.” Praise the steps she used.
When
She counts tiny steps from 0 to find the arrow.
Find halfway first. Then start from the nearest number you know: 0, 50 or 100.
When
On a 0 to 20 line, she says halfway is 50.
“What are the numbers at the ends? Halfway between 0 and 20 is 10.” Read the ends before you start.

Game놀이

Game · Stand on the number

You need: the floor line with only 0 and 100 on it, the 10s cards from Part 1

Call a number: “Stand on 30!” Lia walks along the line and stops where she thinks 30 is.
She says why: “30 is less than halfway, so I am closer to 0.”
Check with the 10s cards. Close counts as a win! Then swap: you stand somewhere, and Lia estimates your number.

Extra challenge더 도전

On a line from 0 to 50, where is halfway? Mark 30.
On a line from 20 to 40, which number is halfway?

In the workbook

Estimate arrows on lines from 0 to 100, 0 to 20 and 0 to 50, mark numbers with arrows, and decide if two friends are right.

Teaching Guide · Number lines and estimating · liabooks.com/study

For you D

Everyday English for maths time수학 시간 생활 영어

Useful sentences for giving instructions, praising and helping.

Starting and giving instructions

Say	It means
Let's do some maths.	Start of the session
Get your pencil, please.
Read the question.
Have a go.	Try it (it's OK to make a mistake)
Show me.	Show with objects or fingers
Count with me.
Write the number sentence.	Write 5 + 3 = 8
Fill in the missing number.	Complete the gap
Explain your thinking.	Say how you did it
Check your answer.
Circle the right one.
Underline the maths word.
Take your time.	There is no hurry
Say it in a full sentence.
Point to …
Let's do one together.

Let's do some maths.It meansStart of the session
Get your pencil, please.It means
Read the question.It means
Have a go.It meansTry it (it's OK to make a mistake)
Show me.It meansShow with objects or fingers
Count with me.It means
Write the number sentence.It meansWrite 5 + 3 = 8
Fill in the missing number.It meansComplete the gap
Explain your thinking.It meansSay how you did it
Check your answer.It means
Circle the right one.It means
Underline the maths word.It means
Take your time.It meansThere is no hurry
Say it in a full sentence.It means
Point to …It means
Let's do one together.It means

Praise that helps

Praise the effort and the thinking, not only the right answer. This helps children try hard things.

Praise

“Great thinking!”
“I like how you explained that.”
“You didn't give up. Well done!”
“That's a clever way!”
“You checked your answer. Good job!”
“You used a new maths word!”
“You found the mistake yourself!”
“Brilliant! Can you do another one?”
“You're getting faster!”
“I can see you worked hard.”

When the answer is wrong

Kind words for mistakes

“Nearly! Let's check together.”
“Hmm, let's look again.”
“Can you show me with the counters?”
“What do you notice?”
“Read the question one more time.”
“Mistakes help us learn.”
“That's a good try. What could we change?”
“Are you sure? How can we check?”

Ending the session

Talk about learning

“What did you learn today?”
“What was easy?”
“What was tricky?”
“Which new word did you learn?”
“Can you teach me one thing?”
“What do you want to practise tomorrow?”

How Lia can explain (sentence stems)

Sentence stem	Example
___ and ___ make ___.	7 and 3 make 10.
I have ___. I need ___ more to make 10.	I have 6. I need 4 more to make 10.
The whole is ___. The parts are ___ and ___.	The whole is 13. The parts are 9 and 4.
I know ___, so I know ___.	I know 3 + 4 = 7, so I know 30 + 40 = 70.
___ ones + ___ ones = ___ ones, so ___ tens + ___ tens = ___ tens.	2 ones + 5 ones = 7 ones, so 2 tens + 5 tens = 7 tens.
First I ___. Then I ___.	First I made 10. Then I added 3.
I think ___ is right / wrong because ___.	I think Amir is wrong because 20 + 50 is 70.
The answer is ___ because ___.	The answer is 9 because 9 + 7 = 16.

___ and ___ make ___.Example7 and 3 make 10.
I have ___. I need ___ more to make 10.ExampleI have 6. I need 4 more to make 10.
The whole is ___. The parts are ___ and ___.ExampleThe whole is 13. The parts are 9 and 4.
I know ___, so I know ___.ExampleI know 3 + 4 = 7, so I know 30 + 40 = 70.
___ ones + ___ ones = ___ ones, so ___ tens + ___ tens = ___ tens.Example2 ones + 5 ones = 7 ones, so 2 tens + 5 tens = 7 tens.
First I ___. Then I ___.ExampleFirst I made 10. Then I added 3.
I think ___ is right / wrong because ___.ExampleI think Amir is wrong because 20 + 50 is 70.
The answer is ___ because ___.ExampleThe answer is 9 because 9 + 7 = 16.

Counting time

Short sentences you can use every day.

Say	It means
Let's count together.
Your turn.
Keep going.	Continue
Start at …
Stop at …
Count up / count down.	Forwards / backwards
Louder, please!
Say it after me.	Repeat
What comes next?
What comes before …?
Write the number I say.	Dictation
How do you spell …?
Cover it and write it.	Spelling practice
Check with the 100 square.
Beat your score!	Try to get more right
That's a new record!	Best score

Let's count together.It means
Your turn.It means
Keep going.It meansContinue
Start at …It means
Stop at …It means
Count up / count down.It meansForwards / backwards
Louder, please!It means
Say it after me.It meansRepeat
What comes next?It means
What comes before …?It means
Write the number I say.It meansDictation
How do you spell …?It means
Cover it and write it.It meansSpelling practice
Check with the 100 square.It means
Beat your score!It meansTry to get more right
That's a new record!It meansBest score

Praise for counting

“Great counting!”
“You didn't stop once!”
“You got past 100!”
“Beautiful spelling!”
“You beat your score!”
“Your English is getting better every day!”
“You worked it out yourself!”

Teaching Guide · Number lines and estimating · liabooks.com/study

이 세트의 단어

about — close to, but not exactly
arrow — a pointer that shows a place on a number line
closer to — a shorter distance away
estimate — a number that is close; it does not have to be exact
halfway — in the middle, the same distance from both ends
interval — the gap between two marks on a number line
label — write the numbers in the right places
number line — a line with numbers in order; small numbers on the left, big numbers on the right

Teaching Guide · Number lines and estimating · liabooks.com/study

On one page

Part	Topic	The big idea in one line	Key words	Workbook
Part 1	10s on a number line	Count in 10s along the line. Each interval is worth 10.	number line, interval, label	10s on the line
Part 2	10s and 1s on a number line	47 is between 40 and 50. Start at the nearest 10, not at 0.	between, closer to, count on	10s and 1s
Part 3	What is each step worth?	Count the intervals between two numbers. A step can be 1, 2, 5 or 10.	interval, worth	What is each step worth?
Part 4–6	Estimate on a number line	Find halfway. Which end is closer? A good estimate is close.	estimate, about, halfway	Estimate the arrow, Mark the number, Think about it

Part 1Topic10s on a number lineThe big idea in one lineCount in 10s along the line. Each interval is worth 10.Key wordsnumber line, interval, labelWorkbook10s on the line
Part 2Topic10s and 1s on a number lineThe big idea in one line47 is between 40 and 50. Start at the nearest 10, not at 0.Key wordsbetween, closer to, count onWorkbook10s and 1s
Part 3TopicWhat is each step worth?The big idea in one lineCount the intervals between two numbers. A step can be 1, 2, 5 or 10.Key wordsinterval, worthWorkbookWhat is each step worth?
Part 4–6TopicEstimate on a number lineThe big idea in one lineFind halfway. Which end is closer? A good estimate is close.Key wordsestimate, about, halfwayWorkbookEstimate the arrow, Mark the number, Think about it

Every day, ask these three questions

Question 1
“What is each interval worth?”
Question 2
“Where is halfway?”
Question 3
“Explain how you know.”

Next in class

Next: Compare and order numbers →

Teaching Guide · Number lines and estimating · liabooks.com/study