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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.

You do not need perfect English. Short, clear sentences are the best sentences for a 7-year-old.

Made by Lia's dad with the help of AI. It follows the White Rose Maths Year 2 scheme (Autumn Block 2, steps 1–6), which Lia's school uses. It is home practice, not official school 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. If you understand it, you can explain it in many ways.
Get ready	Things to put on the table before you start: coins, Lego, paper, 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. Use many of them. Lia will hear all of them at school.
Good questions to ask	Questions that make Lia think and explain. The school wants children to explain, not only to answer.
If Lia is stuck	Common mistakes and what to say.
Game	A short game with no paper. Good for the car, the dinner table or bedtime.
Extra challenge	Harder questions for when Lia finds it easy.

The big ideaWhat it is forThe one thing Lia must understand. Read this first. If you understand it, you can explain it in many ways.
Get readyWhat it is forThings to put on the table before you start: coins, Lego, paper, 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. Use many of them. Lia will hear all of them at school.
Good questions to askWhat it is forQuestions that make Lia think and explain. The school wants children to explain, not only to answer.
If Lia is stuckWhat it is forCommon mistakes and what to say.
GameWhat it is forA short game with no paper. Good for the car, the dinner table or bedtime.
Extra challengeWhat it is forHarder questions for when Lia finds it easy.

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

Time	What to do
2 minutes	Warm up. Count together, or play one quick game from this guide.
5 minutes	Teach the big idea with objects (coins, Lego, fingers). Use the “Teach it” steps.
8–10 minutes	Workbook. Let Lia work. Sit next to her. Ask questions. Do not give the answer too fast.
2 minutes	Talk. “What did you learn today? What was easy? What was tricky?”

2 minutesWhat to doWarm up. Count together, or play one quick game from this guide.
5 minutesWhat to doTeach the big idea with objects (coins, Lego, fingers). Use the “Teach it” steps.
8–10 minutesWhat to doWorkbook. Let Lia work. Sit next to her. Ask questions. Do not give the answer too fast.
2 minutesWhat to doTalk. “What did you learn today? What was easy? What was tricky?”

About languages

The goal is for Lia to know the maths in English, because her lessons are in English. If she 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.

Five golden rules

Objects first, then pictures, then numbers. Even when Lia knows the answer, let her show it with objects sometimes.
Ask “How do you know?” A right answer is good. A right answer with a reason is better.
Wait. Count to five in your head before you help. Thinking time is learning time.
Mistakes are useful. Say “Let's check together”, not “No, wrong.”
Stop while it is still fun. A short happy lesson is better than a long tired one.

On one page

Put this on the fridge.

Part	Topic	The big idea in one line	Key words	Workbook
C	Maths words	Many words mean + and many words mean −.	total, altogether, left, difference	My Maths Words, More Maths Words, Word Detective
Part 1	Bonds to 10	7 and 3 make 10.	bond, make 10, how many more	Bonds to 10
Part 2	Fact families	9, 4, 13 → four facts.	whole, part, fact family	Fact families
Part 3	Related facts	3 + 4 = 7, so 30 + 40 = 70.	ones, tens	Related facts
Part 4	Bonds to 100	4 + 6 = 10, so 40 + 60 = 100.	bond to 100, tens	Bonds to 100
Part 5	Add and subtract 1s	34 + 3 = 37. Only the ones change.	ones digit, tens digit	Add and subtract 1s
Part 6–7	Make 10 · Stories	8 + 5 = 8 + 2 + 3 = 13. Find the word, then the sign.	partition, then	Add by making 10, Story Problems, How did I do?

CTopicMaths wordsThe big idea in one lineMany words mean + and many words mean −.Key wordstotal, altogether, left, differenceWorkbookMy Maths Words, More Maths Words, Word Detective
Part 1TopicBonds to 10The big idea in one line7 and 3 make 10.Key wordsbond, make 10, how many moreWorkbookBonds to 10
Part 2TopicFact familiesThe big idea in one line9, 4, 13 → four facts.Key wordswhole, part, fact familyWorkbookFact families
Part 3TopicRelated factsThe big idea in one line3 + 4 = 7, so 30 + 40 = 70.Key wordsones, tensWorkbookRelated facts
Part 4TopicBonds to 100The big idea in one line4 + 6 = 10, so 40 + 60 = 100.Key wordsbond to 100, tensWorkbookBonds to 100
Part 5TopicAdd and subtract 1sThe big idea in one line34 + 3 = 37. Only the ones change.Key wordsones digit, tens digitWorkbookAdd and subtract 1s
Part 6–7TopicMake 10 · StoriesThe big idea in one line8 + 5 = 8 + 2 + 3 = 13. Find the word, then the sign.Key wordspartition, thenWorkbookAdd by making 10, Story Problems, How did I do?

Every day, ask these three questions

Question 1
“How do you know?”
Question 2
“Can you say it another way?”
Question 3
“Which word helped you?”

Next in class

After these six steps, the class will add and subtract across 10 (for example 38 + 5, 42 − 6), add and subtract tens, and then add and subtract two 2-digit numbers. Bonds to 10 and making 10 are the tools for all of these. If Lia knows her bonds to 10 very well, the next steps will be much easier.

Teaching Guide · Bonds to 10 and fact families · 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 · Bonds to 10 and fact families · 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.”

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

C · Workbook pages 2–4

Maths words: + words and − words덧셈·뺄셈을 뜻하는 영어 말

This is the most important chapter for Lia. She knows the maths. She needs the words.

한국어 요약

덧셈(+)과 뺄셈(−)을 뜻하는 영어 낱말을 정리했어요. total, left, difference처럼 헷갈리기 쉬운 말을 아이에게 어떻게 설명할지, 문장제에서 부호를 스스로 고르게 돕는 질문과 놀이를 담았어요.

The big idea핵심

In English, many different words mean + and many different words mean −. A story problem does not show the sign. The child must find the maths word and choose the sign herself.

Words that mean add ( + )

Word	What it means	Example sentence
add	put numbers together	Add 3 to 5. / 5 add 3 is 8.
plus	the name of the + sign	5 plus 3 equals 8.
and … make	two parts make a whole	5 and 3 make 8.
total	the number of all of them together	The total is 8. What is the total?
altogether	all together (one word!)	How many sweets are there altogether?
sum	the answer when we add	The sum of 5 and 3 is 8.
more than	a bigger number by this much	3 more than 5 is 8.
increase	make bigger	Increase 5 by 3. (You will see this later.)
now (after more come)	the new number after adding	3 more birds come. How many birds are there now?

addWhat it meansput numbers togetherExample sentenceAdd 3 to 5. / 5 add 3 is 8.
plusWhat it meansthe name of the + signExample sentence5 plus 3 equals 8.
and … makeWhat it meanstwo parts make a wholeExample sentence5 and 3 make 8.
totalWhat it meansthe number of all of them togetherExample sentenceThe total is 8. What is the total?
altogetherWhat it meansall together (one word!)Example sentenceHow many sweets are there altogether?
sumWhat it meansthe answer when we addExample sentenceThe sum of 5 and 3 is 8.
more thanWhat it meansa bigger number by this muchExample sentence3 more than 5 is 8.
increaseWhat it meansmake biggerExample sentenceIncrease 5 by 3. (You will see this later.)
now (after more come)What it meansthe new number after addingExample sentence3 more birds come. How many birds are there now?

Words that mean subtract ( − )

Word	What it means	Example sentence
subtract	take one number from another	Subtract 3 from 8. (Start with 8!)
minus	the name of the − sign	8 minus 3 equals 5.
take away	remove some	8 take away 3 is 5.
left	what stays after some go	How many are left?
fewer than / less than	a smaller number by this much	3 fewer than 8 is 5. 3 less than 8 is 5.
difference	how far apart two numbers are	The difference between 8 and 5 is 3.
decrease	make smaller	Decrease 8 by 3. (Later.)
action words	things go away	fly away, eat, give away, pop, lose, spend, get off (a bus)

subtractWhat it meanstake one number from anotherExample sentenceSubtract 3 from 8. (Start with 8!)
minusWhat it meansthe name of the − signExample sentence8 minus 3 equals 5.
take awayWhat it meansremove someExample sentence8 take away 3 is 5.
leftWhat it meanswhat stays after some goExample sentenceHow many are left?
fewer than / less thanWhat it meansa smaller number by this muchExample sentence3 fewer than 8 is 5. 3 less than 8 is 5.
differenceWhat it meanshow far apart two numbers areExample sentenceThe difference between 8 and 5 is 3.
decreaseWhat it meansmake smallerExample sentenceDecrease 8 by 3. (Later.)
action wordsWhat it meansthings go awayExample sentencefly away, eat, give away, pop, lose, spend, get off (a bus)

Tricky words — read this carefully

Tricky word	Why it is tricky	How to explain it
more	“3 more than 5” means add. But “How many more does Sam have?” means find the difference (subtract).	Ask: “Are we making it bigger? Or are we comparing two numbers?”
gives	“Lia gives 7 to Sam” — Lia has fewer (−). “Sam gives Lia 5” — Lia has more (+).	Ask: “Who gets the things? Does Lia get more, or does she have fewer?”
subtract … from	“Subtract 3 from 8” is 8 − 3, not 3 − 8. The order in the sentence is back to front.	Say: “From means start here. Start with 8.”
difference	In everyday English, difference means “not the same”. In maths, it is a number.	Build two towers. “How many more bricks is the tall tower? That number is the difference.”
sum	In everyday British English, “doing sums” means any maths. In a maths question, “the sum” means the answer to an adding.	“The sum is the answer when we add.”
fewer / less	Teachers say fewer for things you can count (fewer apples) and less for things you cannot count (less water). Lia will hear both.	Both mean the number is smaller.
left	Left is also a direction (left and right).	“Left here means: still here, not gone.”

moreWhy it is tricky“3 more than 5” means add. But “How many more does Sam have?” means find the difference (subtract).How to explain itAsk: “Are we making it bigger? Or are we comparing two numbers?”
givesWhy it is tricky“Lia gives 7 to Sam” — Lia has fewer (−). “Sam gives Lia 5” — Lia has more (+).How to explain itAsk: “Who gets the things? Does Lia get more, or does she have fewer?”
subtract … fromWhy it is tricky“Subtract 3 from 8” is 8 − 3, not 3 − 8. The order in the sentence is back to front.How to explain itSay: “From means start here. Start with 8.”
differenceWhy it is trickyIn everyday English, difference means “not the same”. In maths, it is a number.How to explain itBuild two towers. “How many more bricks is the tall tower? That number is the difference.”
sumWhy it is trickyIn everyday British English, “doing sums” means any maths. In a maths question, “the sum” means the answer to an adding.How to explain it“The sum is the answer when we add.”
fewer / lessWhy it is trickyTeachers say fewer for things you can count (fewer apples) and less for things you cannot count (less water). Lia will hear both.How to explain itBoth mean the number is smaller.
leftWhy it is trickyLeft is also a direction (left and right).How to explain it“Left here means: still here, not gone.”

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Read the word pages together (workbook: My Maths Words and More Maths Words)

YOU“Let's read these words. I read one, you read one.”

YOU“Which colour are the add words? Which colour are the take-away words?”

YOU“Can you find a word that means add? Can you find another one?”

Same maths, different words

YOU“Look: 5 + 3 = 8. How many ways can we say it?”

LIA5 add 3 is 8. 5 plus 3 equals 8…

YOU“Great! Can you say it with the word total? With the word more?”

YOU“Now let's do 8 − 3 = 5. Can you say it with take away? With left?”

Word detective (workbook: Word Detective)

YOU“I will say a sentence. Show me a thumbs up for add, or a thumbs down for take away.”

YOU“How many are left?”

LIAThumbs down!

YOU“Yes! Which word helped you?”

LIALeft.

Ways to ask “add or subtract?”표현

“Is it add or take away?”
“Is it plus or minus?”
“Will the number get bigger or smaller?”
“Which word tells you?”
“What is the maths word here?”
“Do we put them together or take some away?”

Good questions to ask좋은 질문

“Which word helped you?”
Note
This is the key question of this whole set.
“Can you say it another way?”
Note
Makes Lia use new words.
“Will the answer be bigger or smaller than the first number?”
Note
Helps her check the sign.
“Can you make a sentence with the word ‘altogether’?”
Note
Using a word is harder than reading it.

If Lia is stuck막힐 때

When
Lia chooses + because she sees a number getting bigger somewhere in the story.
Ask her to act it out with toys. “Show me. Do the toys come or go?”
When
She knows the maths but not the word (for example ‘difference’).
Show the meaning with objects, say the word, and ask her to say it back. Add it to a word list on the fridge.
When
She mixes up ‘left’ (direction) and ‘left’ (still here).
Say both with actions: point left, then hide some toys and say “These are left.”

Games (2)놀이

Game · Thumbs up, thumbs down

You need: nothing

You say a maths sentence, for example “4 birds fly away.”
Lia shows thumbs up for + and thumbs down for −.
She must say the word that helped her.
Swap: Lia makes a sentence, you show the thumb.

Game · Word hunt

You need: a book, a menu or a shop sign

Look for maths words in real life: more, less, total, left, altogether.
When Lia finds one, she reads the sentence and tells you if it means + or −.
Supermarket receipts are great: they always have a “TOTAL”.

In the workbook

Word pages and the Word Detective page.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 1 · Step 1 · Workbook pages 5–6

Bonds to 1010의 보수

Two numbers that make 10.

한국어 요약

더해서 10이 되는 두 수(number bonds to 10)를 영어로 가르치는 법이에요. 손가락과 10칸 상자, 숨기기 놀이로 시작하는 대본, 같은 질문을 다르게 묻는 영어 표현, 막힐 때 할 말을 담았어요.

The big idea핵심

A number bond to 10 is a pair of numbers that make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5. In Year 2, Lia should know these instantly, without counting. They are used again and again: in making 10 (Part 6), in bonds to 100 (Part 4), and in bigger adding later.

6 and 4 make 10

8 and 2 make 10

5 and 5 make 10

Get ready준비물

10 small things (coins, beads, Lego) in two colours if possible
An egg box with 10 cups, or a ten frame drawn on paper
A cup to hide things under
Your ten fingers!

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Fingers warm-up

YOU“Show me 10 fingers.”

YOU“Now put 3 fingers down. How many fingers are up?”

LIA7.

YOU“Yes. 7 fingers up and 3 fingers down. 7 and 3 make 10.”

YOU“Let's do it again. Put 6 fingers down…”

Do this 4–5 times, quickly. Fingers are the best ten frame: we always carry them!

Ten frame

DOPut 7 counters in the ten frame. Fill the top row first.

YOU“How many counters?”

LIA7.

YOU“How many empty spaces?”

LIA3.

YOU“So 7 and 3 make 10. We write it like this: 7 + 3 = 10.”

YOU“Can you say it? ‘7 plus 3 equals 10.’”

The hiding game

DOShow 10 counters. Hide some under a cup. Leave the rest outside.

YOU“There are 10 altogether. I can see 4. How many are hiding under the cup?”

LIA6!

YOU“How do you know?”

LIABecause 4 and 6 make 10.

YOU“Let's check!”

DOLift the cup and count together.

Find all the bonds, and the pattern

YOU“Let's write every bond to 10. Start with 0 + 10.”

YOU“What comes next?”

YOU“What do you notice?”

LIAThis number goes up and that number goes down.

YOU“Yes! When one number goes up by 1, the other goes down by 1. The total stays 10.”

From adding to taking away

YOU“If 7 + 3 = 10, what is 10 − 3?”

LIA7.

YOU“And 10 − 7?”

LIA3.

YOU“Good. Bonds help us take away too.”

Good questions to ask좋은 질문

“How do you know?”
Good answers
“Because 7 and 3 make 10.” / “I counted the empty spaces.”
“Can you show me with your fingers?”
“If 7 + 3 = 10, what is 3 + 7?”
Note
Adding can be done in any order.
“Which bond to 10 is a double?”
Note
5 + 5. A double means the same number twice.
“Is 6 + 3 a bond to 10? Why not?”
Note
No, 6 + 3 = 9. Reasoning question.

If Lia is stuck막힐 때

When
Lia counts from 1 every time.
That is fine at first. Then say: “Don't count the counters. Count the empty spaces.” Later: “Can you just know it?”
When
She says 6 + 3 = 10.
Use fingers: “Show me 6. Now 3 more. How many fingers?” Let her find the mistake herself.
When
She forgets 0 + 10 and 10 + 0.
Show a full ten frame. “How many empty spaces? 0. So 10 + 0 = 10.”

Games (2)놀이

Game · Bond ping-pong

You need: nothing

You say a number from 0 to 10: “Four!”
Lia says the partner as fast as she can: “Six!”
Then Lia says a number and you answer. Make a funny mistake sometimes. Can she catch you?

Game · Make 10 card game

You need: playing cards: Ace (=1) to 9, plus the 10s

Put 12 cards face up.
Take turns. Find two cards that make 10 (for example 3 and 7). Say the number sentence: “3 plus 7 equals 10.” Keep the pair.
A 10 card can be taken alone: “10 plus 0 equals 10.”
Add new cards. The player with the most pairs wins.

Extra challenge더 도전

Three numbers that make 10: 2 + 3 + 5 = 10. How many can you find?
Bonds to 20: 7 + 13 = 20. “What do you notice? 7 + 3 = 10 and 7 + 13 = 20.”
Missing numbers: 10 = ? + 8, 10 − ? = 4.

In the workbook

Ten frames, missing numbers, all the bonds to 10, and three short stories.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 2 · Step 2 · Workbook pages 7–8

Fact families수 가족

Three numbers, four facts.

한국어 요약

세 수로 덧셈 두 개와 뺄셈 두 개를 만드는 수 가족(fact family)을 영어로 가르치는 법이에요. whole과 part라는 말, 뺄셈은 늘 전체에서 시작한다는 점을 작은 물건과 부분-전체 그림으로 보여 줘요.

The big idea핵심

Three numbers like 9, 4 and 13 make a fact family. They give four facts: 9 + 4 = 13, 4 + 9 = 13, 13 − 4 = 9, 13 − 9 = 4. Adding and subtracting are opposites: one puts together, one takes apart. We can add in any order, but when we subtract we must start with the whole (the biggest number).

whole 13, parts 9 and 4

the same family as a bar model

Get ready준비물

13 counters in two colours (9 of one colour, 4 of another)
Paper with a part–whole model drawn on it (three circles)
A pencil

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Make the whole and the parts

DOPut 9 red and 4 blue counters in the whole circle.

YOU“How many altogether?”

LIA13.

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

DOMove the red ones to one part circle and the blue ones to the other.

YOU“Now we have two parts. The parts are 9 and 4.”

Two adding facts

YOU“9 and 4 make 13. So 9 + 4 = 13.”

YOU“Can we start with 4? 4 and 9 make…?”

LIA13 too!

YOU“Yes! We can add in any order. The answer is the same.”

Two taking-away facts

DOPut all 13 back in the whole. Now take away the 4 blue ones.

YOU“What is left?”

LIA9.

YOU“So 13 − 4 = 9. Now start again and take away the 9 red ones. What is left?”

LIA4.

YOU“So 13 − 9 = 4.”

Why we start with the whole

YOU“Can we do 4 − 13?”

LIANo…

YOU“In Year 2 we always start with the whole, the biggest number. The whole goes first when we take away.”

Write the family

YOU“Let's write all four facts. Two with plus and two with minus.”

YOU“Which number is in every fact?”

YOU“Which number is always first in the minus facts?”

LIA13, the whole.

Other ways to say it다른 표현

“What is the whole?”
“What are the parts?”
“The whole is 13. One part is 9. What is the other part?”
“Write the fact family for 9, 4 and 13.”
“If you know 9 + 4 = 13, what else do you know?”
“Can you write a related fact?”
“Can you write it the other way round?”

Good questions to ask좋은 질문

“If you know 9 + 4 = 13, what else do you know?”
Note
The best question for this topic. Aim for all three other facts.
“Is 13 − 4 = 9 true or false? How do you know?”
“Which number is the whole? How can you tell?”
Note
It is the biggest one.
“Why does 4 + 9 give the same answer as 9 + 4?”
Good answers
“They are the same parts, just in a different order.”
“Is 4 − 13 = 9 true?”
Note
False. Explain: we start with the whole.

If Lia is stuck막힐 때

When
She writes 4 − 13 = 9.
Point to the part–whole model. “Where do we start when we take away? At the top, the whole.”
When
She writes only 2 or 3 facts.
“A family has four people: two plus facts and two minus facts. Who is missing?”
When
She does not know which number is the whole.
“The whole is made of the parts, so it is the biggest.” Show it with counters.

Games (2)놀이

Game · Fact family houses

You need: paper and pens

Draw a house. Write the whole (for example 12) in the roof.
Draw two doors with the parts (7 and 5).
Draw four windows. Lia writes one fact in each window.
Then Lia makes a house for you. Make one mistake on purpose. Can she find it?

Game · Mystery part

You need: counters and a cup

Show 11 counters: “The whole is 11.”
Hide some under the cup. Show 5: “One part is 5. What is the mystery part?”
Lia answers with a full sentence: “The mystery part is 6, because 5 and 6 make 11.”

Extra challenge더 도전

Families with bigger numbers: 30, 40 and 70. (“30 + 40 = 70, 40 + 30 = 70, 70 − 40 = 30, 70 − 30 = 40.”)
Can a fact family have only two facts? Yes, when the parts are the same: 5 + 5 = 10 and 10 − 5 = 5.
Find a fact family where the whole is 20.

In the workbook

Part–whole models, bar models, true or false, and a story about marbles.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 3 · Step 3 · Workbook pages 9

Related facts이어지는 계산식

If 3 + 4 = 7, then 30 + 40 = 70.

한국어 요약

3 + 4 = 7을 알면 30 + 40 = 70도 풀 수 있다는 것을 영어로 가르치는 법이에요. 20 + 50 = 700 같은 실수를 tens라는 말로 바로잡고, thirteen과 thirty처럼 헷갈리는 발음도 함께 연습해요.

The big idea핵심

Lia can use a small fact to find a big fact. 3 ones + 4 ones = 7 ones, so 3 tens + 4 tens = 7 tens. 7 tens is 70. So 30 + 40 = 70. We are counting tens in the same way we count ones or apples. A common mistake is 20 + 50 = 700. Talking about “tens” stops this mistake.

3 ones + 4 ones = 7 ones

3 tens + 4 tens = 7 tens = 70

Get ready준비물

Lego towers of 10 (or bundles of 10 straws or ice-cream sticks)
Some single bricks
Coins: 10 sen coins are perfect. Each one is a ten.

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Things, not only numbers

YOU“3 apples and 4 apples make…?”

LIA7 apples.

YOU“3 cars and 4 cars make…?”

LIA7 cars.

YOU“3 tens and 4 tens make…?”

LIA7 tens!

YOU“Yes! It works for apples, cars and tens.”

Show with tens

DOGive 3 towers of 10.

YOU“Each tower is 1 ten. How many tens are here?”

LIA3 tens.

YOU“3 tens is 30. Let's count: 10, 20, 30.”

DOAdd 4 more towers.

YOU“Now how many tens?”

LIA7 tens.

YOU“7 tens is 70. So 30 + 40 = 70.”

Use money

DOShow three 10 sen coins and four 10 sen coins.

YOU“How much money is this?”

LIA70 sen.

YOU“3 coins and 4 coins make 7 coins. Each coin is 10 sen. So 30 sen + 40 sen = 70 sen.”

Taking away tens

YOU“8 − 3 = 5. So 80 − 30 = …?”

LIA50.

YOU“How do you know?”

LIA8 tens take away 3 tens is 5 tens. 5 tens is 50.

Spot the mistake

YOU“Amir says 20 + 50 = 700. Is he right?”

LIANo!

YOU“Why not?”

LIA2 tens and 5 tens make 7 tens. 7 tens is 70, not 700.

Say the numbers clearly

Tens numbers and teen numbers sound similar. Say them slowly, and practise with Lia:

Teen number	Tens number	How to hear the difference
13 thirTEEN	30 THIRty	Teen numbers are strong at the end. Tens numbers are strong at the start.
14 fourTEEN	40 FORty	Spelling: forty has no u (not fourty).
15 fifTEEN	50 FIFty
16 sixTEEN	60 SIXty
17 sevenTEEN	70 SEVenty
18 eighTEEN	80 EIGHty
19 nineTEEN	90 NINEty

13 thirTEENTens number30 THIRtyHow to hear the differenceTeen numbers are strong at the end. Tens numbers are strong at the start.
14 fourTEENTens number40 FORtyHow to hear the differenceSpelling: forty has no u (not fourty).
15 fifTEENTens number50 FIFtyHow to hear the difference
16 sixTEENTens number60 SIXtyHow to hear the difference
17 sevenTEENTens number70 SEVentyHow to hear the difference
18 eighTEENTens number80 EIGHtyHow to hear the difference
19 nineTEENTens number90 NINEtyHow to hear the difference

Other ways to say it다른 표현

“3 tens add 4 tens”
“thirty plus forty”
“What is 30 more than 40?”
“What is 40 add 30?”
“How many tens is 70?”
“What is 20 less than 90?”
“Use 5 − 2 to help you find 50 − 20.”

Good questions to ask좋은 질문

“Which small fact helps you?”
Note
For 60 + 30, the small fact is 6 + 3.
“How many tens is 90?”
“Why is 20 + 50 not 700?”
Note
Reasoning question. Use the word tens in the answer.
“What do you notice? 100 − 10, 100 − 20, 100 − 30…”
Note
The answers go down in tens: 90, 80, 70.

If Lia is stuck막힐 때

When
She writes 20 + 50 = 7.
“7 what? 7 ones or 7 tens?” Show 7 towers.
When
She writes 700.
Build it with towers. “Count the tens with me: 10, 20, 30, … 70.”
When
She confuses 17 and 70 when you speak.
Say the number, then write it. Use the table above.

Game놀이

Game · Tens shop

You need: 10 sen coins (or paper coins) and some toys with price tags: 20 sen, 30 sen, 50 sen…

Lia is the shopkeeper. You buy two toys: “I want the 30 sen car and the 40 sen ball. How much is that altogether?”
Lia uses the small fact: 3 + 4 = 7, so 70 sen.
Give her 90 sen: “How much change?” (90 − 70 = 20). Swap roles.

Extra challenge더 도전

Hundreds: 300 + 400 = 700. “3 hundreds and 4 hundreds make 7 hundreds.”
Missing number: 60 + ? = 90.
Three tens numbers: 20 + 30 + 40 = ?

In the workbook

Use a small fact, base 10 pictures, the ‘700’ mistake, and a pattern.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 4 · Step 4 · Workbook pages 10

Bonds to 100100의 보수

4 + 6 = 10, so 40 + 60 = 100.

한국어 요약

4 + 6 = 10이니 40 + 60 = 100이라는 것, 몇십과 몇십으로 100을 만드는 법을 영어로 가르쳐요. 손가락 하나를 10으로 세는 대본과 10센 동전으로 1링깃을 만드는 놀이를 담았어요.

The big idea핵심

100 is 10 tens. So bonds to 100 (with tens) are just bonds to 10, but with tens: 1 + 9 = 10, so 10 + 90 = 100; 4 + 6 = 10, so 40 + 60 = 100. This joins Part 1 (bonds to 10) and Part 3 (related facts).

4 tens and 6 tens make 10 tens = 100

Get ready준비물

10 towers of 10 Lego bricks (or 10 bundles of straws)
Ten 10 sen coins, and a RM1 coin or note to compare
Your ten fingers (each finger can be a ten!)

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

How many tens make 100?

DOPut out 10 towers. Count them together in tens: 10, 20, 30 … 100.

YOU“How many towers did we count?”

LIA10.

YOU“So 10 tens make 100.”

Fingers are tens

YOU“Show me 10 fingers. Now each finger is worth 10.”

YOU“Put 4 fingers down. How many tens are down? And how many tens are up?”

LIA4 tens are down. 6 tens are up.

YOU“4 tens is 40. 6 tens is 60. 40 and 60 make 100.”

Money

DOShow ten 10 sen coins.

YOU“Ten 10 sen coins make 100 sen. 100 sen is 1 ringgit.”

YOU“I have 70 sen. How much more do I need to make 1 ringgit?”

LIA30 sen.

YOU“How do you know?”

LIA7 and 3 make 10, so 70 and 30 make 100.

Taking away from 100

YOU“If 40 + 60 = 100, what is 100 − 60?”

LIA40.

YOU“And 100 − 40?”

LIA60.

Other ways to say it다른 표현

“What goes with 70 to make 100?”
“70 and what make 100?”
“How many more to make 100?”
“How many tens make 100?”
“What is the bond to 100 for 30?”
“100 take away 30 is?”
“What do I need to add to 20 to get 100?”

Good questions to ask좋은 질문

“How many tens are in 100?”
Note
10.
“Which bond to 10 helps you find 30 + ? = 100?”
Note
3 + 7 = 10.
“What do you notice about bonds to 10 and bonds to 100?”
Good answers
“They are the same, but with tens.”
“Is 50 + 50 = 100 true? Why?”

If Lia is stuck막힐 때

When
She says 40 + 60 = 10.
“10 what? 10 ones or 10 tens?” Build it: 4 towers and 6 towers.
When
She says 30 + 80 = 100.
Check the small fact: 3 + 8 is not 10. “Which number goes with 3 to make 10?”
When
She tries to count on in ones from 70.
Say: “Count in tens: 80, 90, 100. How many jumps?”

Game놀이

Game · Race to 1 ringgit

You need: ten 10 sen coins each (or paper coins) and one dice

Take turns to roll the dice. Take that many 10 sen coins. Say how much you have: “I have 40 sen.”
Before each roll, say how much more you need: “I need 60 sen more to make 1 ringgit.”
If your roll takes you past 100 sen, you miss that turn. The first player to make exactly 100 sen (1 ringgit) wins.

Extra challenge더 도전

Bonds to 100 with ones (Year 3 work, only if she finds it easy): 35 + 65 = 100. Hint: “The ones make 10, and the tens make 90.”
Three tens numbers that make 100: 20 + 30 + 50.
Bonds to 1000: 400 + 600 = 1000.

In the workbook

Bars of tens, missing numbers, and two stories.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 5 · Step 5 · Workbook pages 11

Add and subtract 1s일의 자리 더하고 빼기

34 + 3 = 37. Only the ones change.

한국어 요약

34 + 3 = 37처럼 일의 자리만 바뀌는 덧셈과 뺄셈을 영어로 가르치는 법이에요. tens digit, ones digit이라는 말과 자릿값 생각을 블록으로 보여 주고, 10을 넘지 않는 수로 연습해요.

The big idea핵심

When we add or take away a few ones, and the ones do not go past 10, only the ones digit changes. The tens stay the same. For example: 34 has 3 tens and 4 ones. 4 ones + 3 ones = 7 ones. So 34 + 3 = 37. This is about place value: the tens digit and the ones digit have different jobs.

34 + 3 = 37

Get ready준비물

Lego towers of 10 and single bricks
A pencil and paper
Numbers where the ones do not pass 10 (like 42 + 5 or 67 − 4). Crossing 10 is the next step!

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Build the number

DOBuild 34 with 3 towers and 4 single bricks.

YOU“How many tens? How many ones?”

LIA3 tens and 4 ones.

YOU“The tens digit is 3. The ones digit is 4.”

Add some ones

DOAdd 3 single bricks.

YOU“What changed? The tens or the ones?”

LIAThe ones.

YOU“How many ones now?”

LIA7.

YOU“So 34 + 3 = 37. The tens digit stayed 3.”

Take away some ones

DOBuild 58. Take away 5 single bricks.

YOU“How many ones are left?”

LIA3.

YOU“Did the tens change?”

LIANo.

YOU“So 58 − 5 = 53.”

Look for the pattern

YOU“41 + 1 = 42. 41 + 2 = 43. 41 + 3 = 44.”

YOU“What do you notice?”

LIAThe ones go up by one. The tens don't change.

YOU“Now 58 − 1, 58 − 2, 58 − 3…”

Only numbers

YOU“Can you do 82 + 7 in your head?”

LIA89.

YOU“How did you do it?”

LIA2 add 7 is 9, and the 8 tens stay.

Other ways to say it다른 표현

“What is 3 more than 34?”
“What is 5 less than 58?”
“34 add 3”
“58 take away 5”
“What changes: the tens or the ones?”
“What is the ones digit now?”
“Which digit stays the same?”
“Count on 3 from 34.”
“Count back 5 from 58.”

Good questions to ask좋은 질문

“Which digit changes? Which digit stays the same?”
“Why does the tens digit stay the same?”
Good answers
“Because we only added ones, and the ones did not make a new ten.”
“What is the same about 23 + 4 and 3 + 4?”
Note
The ones fact is the same: 3 + 4 = 7.
“Is 64 + 4 = 104 true?”
Note
False. It is 68. Only the ones change.

If Lia is stuck막힐 때

When
She adds to the tens: 34 + 3 = 64.
“Is it 3 ones or 3 tens?” Build it. Single bricks are ones.
When
She counts on in ones from 1.
“Start at 34. Put 34 in your head. Now count on 3: 35, 36, 37.”
When
She reads 34 as 43.
Point: “Tens first, then ones.” Build it with towers.
When
You chose a number that crosses 10, like 38 + 5.
That is the next step. If Lia can do it, great! Show her Part 6: make 10 first.

Games (2)놀이

Game · Number spy

You need: nothing

Say: “I am thinking of a number. It has 5 tens and 2 ones. What is it?” (52)
“Now I add 4 ones. What is my number?” (56)
“Now I take away 3 ones.” (53). Lia makes a number for you next.

Game · Dice ladder

You need: one dice, paper

Start at 21. Roll the dice and add: 21 + 4 = 25. Write it.
Keep going while the ones stay 9 or less. If a roll would pass 10, the other player takes the turn.
Talk about the rule: “Which rolls can we use when we are at 25?” (1, 2, 3, 4)

Extra challenge더 도전

Add tens instead: 34 + 30 = 64. “Now what changes?” (The tens.)
Two steps: 57 − 4 − 2 = ?
Missing numbers: 64 + ? = 68, ? − 3 = 42.

In the workbook

Base 10 pictures, patterns and two stories.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 6 · Step 6 · Workbook pages 12

Challenge: add by making 10도전: 10을 만들어 더하기

8 + 5 = 8 + 2 + 3 = 13.

한국어 요약

8 + 5를 8 + 2 + 3으로 나눠 먼저 10을 만드는 덧셈(make 10, bridging through 10)을 영어로 가르쳐요. 10칸 상자 두 개와 수직선으로 보여 주고, 아이가 찾은 다른 방법도 인정해 주는 말을 담았어요.

The big idea핵심

When two numbers add up to more than 10, we can make 10 first. For 8 + 5: 8 needs 2 more to make 10. So we partition (split) 5 into 2 and 3. 8 + 2 = 10. Then 10 + 3 = 13. This uses bonds to 10 and makes hard adding easy. It is also called bridging through 10.

fill the first ten frame, then put the rest in the second

jump to 10, then jump the rest

Get ready준비물

Two ten frames (two egg boxes, or draw two grids)
About 20 counters in two colours
A number line 0–20 (a ruler works)

Teach it, step by step단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

Two ten frames

DOPut 8 green counters in the first ten frame and 5 red counters next to it.

YOU“How many more does the first ten frame need to be full?”

LIA2.

DOMove 2 red counters into the first frame.

YOU“Now the first frame is 10. How many red counters are left outside?”

LIA3.

YOU“10 and 3 make 13. So 8 + 5 = 13.”

Say the steps

YOU“We split 5 into 2 and 3.”

YOU“8 + 2 = 10. Then 10 + 3 = 13.”

YOU“Can you say the steps for 9 + 4?”

LIA9 needs 1. Split 4 into 1 and 3. 9 + 1 = 10. 10 + 3 = 13.

Number line

YOU“Put your finger on 8. Jump to 10. How big is that jump?”

LIA2.

YOU“We need to jump 5 altogether. We jumped 2. How many more?”

LIA3. So we land on 13.

Other ways are OK too

YOU“Did anyone do it a different way?”

LIAI know 8 + 8 is 16, so…

YOU“Great! There are many ways. Which way is fastest for you?”

The school likes children to find more than one way. Praise every correct way. Making 10 is one useful tool.

Other ways to say it다른 표현

“Make 10 first.”
“How many more to make 10?”
“Split the 5 into 2 and 3.”
“Partition the 5.”
“Jump to 10, then jump the rest.”
“Fill the ten frame first.”
“Can you find another way?”

Good questions to ask좋은 질문

“Which number did you split? Why?”
Note
Usually we keep the bigger number and split the smaller one.
“How many does 7 need to make 10?”
“Why does making 10 help?”
Good answers
“Adding to 10 is easy: 10 + 3 = 13.”
“Can you do 6 + 9 by making 10 with the 9?”
Note
9 needs 1: split 6 into 1 and 5. 10 + 5 = 15.

If Lia is stuck막힐 때

When
She does not know which number to split.
“Start with the bigger number. How many does it need to make 10? Take that from the other number.”
When
She forgets the second step (stops at 10).
“You used 2. The 5 had 3 more. Where are they?” Point at the counters.
When
She prefers counting on (8… 9, 10, 11, 12, 13).
That is correct, but slow for bigger numbers. Try both and ask: “Which was quicker?”

Game놀이

Game · Fill the frames

You need: two ten frames each, counters, a dice (or two dice for bigger numbers)

Each player rolls and puts that many counters in their ten frames. Always fill the first frame before the second.
Say your total the ‘make 10’ way: “I had 8, I rolled 5. 2 fill my frame, 3 more. I have 13.”
The first player to fill both frames (20) wins.

Extra challenge더 도전

Make 10 with bigger numbers: 28 + 5 = 28 + 2 + 3 = 33. (This is the next step!)
Take away through 10: 13 − 5 = 13 − 3 − 2 = 8.
Doubles and near doubles: 6 + 7 = 6 + 6 + 1 = 13.

In the workbook

Make 10 with ten frames, quick questions, and a crayon story.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

Part 7 · Workbook pages 13

Story problems이야기로 된 문제(문장제)

Read, picture, find the word, choose the sign, answer.

한국어 요약

영어 문장제를 읽고, 그려 보고, 핵심 낱말을 찾아 +와 − 중 하나를 고르는 다섯 단계 순서를 가르쳐요. gives, rest, more처럼 헷갈리는 표현과 아이가 직접 이야기를 만드는 문장 틀도 담았어요.

The big idea핵심

A story problem is maths inside a short story. The numbers are easy for Lia. The hard part is reading the story and deciding what to do. We teach one routine and use it every time. Lia should also learn to write her own stories: this is the best way to learn the words.

The five-step routine

Step	What Lia does	What you can say
1. Read	Read the whole story. Then read it again.	“Read it two times. The second time, read slowly.”
2. Picture it	Imagine it, act it out with toys, or draw a quick picture or bar model.	“What is happening? Can you show me with toys?”
3. Find the maths word	Underline the word that tells + or −.	“Which word tells you what to do?”
4. Write a number sentence	Choose + or − and write it: 16 − 7 = ?	“Can you write it as a number sentence?”
5. Answer in a sentence	Say the answer with the thing: “Lia has 9 stickers left.”	“9 what? Say it in a full sentence.”

1. ReadWhat Lia doesRead the whole story. Then read it again.What you can say“Read it two times. The second time, read slowly.”
2. Picture itWhat Lia doesImagine it, act it out with toys, or draw a quick picture or bar model.What you can say“What is happening? Can you show me with toys?”
3. Find the maths wordWhat Lia doesUnderline the word that tells + or −.What you can say“Which word tells you what to do?”
4. Write a number sentenceWhat Lia doesChoose + or − and write it: 16 − 7 = ?What you can say“Can you write it as a number sentence?”
5. Answer in a sentenceWhat Lia doesSay the answer with the thing: “Lia has 9 stickers left.”What you can say“9 what? Say it in a full sentence.”

Teach it, step by step (with one story)단계별 수업

YOU 부모가 할 말LIA 아이가 할 만한 대답DO 손으로 할 일

“Lia has 16 stickers. She gives 7 stickers to Sam. How many stickers does Lia have left?”

Read and picture

YOU“Let's read it two times.”

YOU“What is happening in the story?”

LIALia gives stickers to Sam.

YOU“Does Lia have more stickers at the end, or fewer?”

LIAFewer.

Find the word

YOU“Which words tell us what to do?”

LIAGives… and left.

YOU“Yes! She gives some away, and we want to know how many are left. Is that add or take away?”

LIATake away.

Number sentence

YOU“What do we start with?”

LIA16.

YOU“What do we take away?”

LIA7.

YOU“Can you write the number sentence?”

LIA16 − 7 = 9.

Answer and check

YOU“Say the answer in a full sentence.”

LIALia has 9 stickers left.

YOU“Let's check. 9 + 7 = 16. Yes! That's our fact family.”

Watch out for these

Story	Why it is tricky	The maths
Her friend gives her 5 more.	“Gives” but Lia gets more.	+
She gives 7 to Sam.	Lia has fewer.	−
5 are blue. The rest are green.	“The rest” means the other part.	11 − 5 (a missing part)
How many more does Mo have than Amir?	“More”, but we compare two numbers.	12 − 8 (the difference)
How many more are needed to make 100?	Both + and − work!	60 + ? = 100 or 100 − 60
5 people get off the bus. / 5 people get on.	Small words change everything.	get off −, get on +

Her friend gives her 5 more.Why it is tricky“Gives” but Lia gets more.The maths+
She gives 7 to Sam.Why it is trickyLia has fewer.The maths−
5 are blue. The rest are green.Why it is tricky“The rest” means the other part.The maths11 − 5 (a missing part)
How many more does Mo have than Amir?Why it is tricky“More”, but we compare two numbers.The maths12 − 8 (the difference)
How many more are needed to make 100?Why it is trickyBoth + and − work!The maths60 + ? = 100 or 100 − 60
5 people get off the bus. / 5 people get on.Why it is trickySmall words change everything.The mathsget off −, get on +

Make your own stories

Give Lia a number sentence. She makes a story. You help with the English. Start with a story frame:

Frame	Example
There were ___ ___. Then ___ more came. How many ___ are there now?	There were 6 ducks. Then 3 more came. How many ducks are there now?
___ had ___ ___. She gave ___ away. How many are left?	Mum had 10 cookies. She gave 4 away. How many are left?
___ has ___ ___. ___ has ___ ___. How many do they have altogether?	Lia has 5 shells. Dad has 4 shells. How many do they have altogether?
___ has ___. ___ has ___. What is the difference?	Lia has 12 pencils. Dad has 8 pencils. What is the difference?

There were ___ ___. Then ___ more came. How many ___ are there now?ExampleThere were 6 ducks. Then 3 more came. How many ducks are there now?
___ had ___ ___. She gave ___ away. How many are left?ExampleMum had 10 cookies. She gave 4 away. How many are left?
___ has ___ ___. ___ has ___ ___. How many do they have altogether?ExampleLia has 5 shells. Dad has 4 shells. How many do they have altogether?
___ has ___. ___ has ___. What is the difference?ExampleLia has 12 pencils. Dad has 8 pencils. What is the difference?

Real-life stories at home표현

“There are 10 chopsticks. We use 8. How many chopsticks are left?”
“You had 8 grapes. You ate 3. How many are left?”
“This bag has 30 sen. That bag has 40 sen. How much altogether?”
“We need 10 plates. There are 6 on the table. How many more do we need?”
“There are 25 cars in the car park. 4 cars drive away. How many are left?”

Good questions to ask좋은 질문

“What is happening in the story?”
Note
Understanding first, numbers later.
“Will the answer be bigger or smaller than 16?”
Note
A quick check of the sign.
“Can you draw it?”
Note
A bar model or small circles is enough.
“Does your answer make sense?”
Note
If Lia gave stickers away, she can't have more than 16.
“Can you make up a story for 13 − 5?”

If Lia is stuck막힐 때

When
She picks numbers and adds them without reading.
Cover the numbers with your finger. “What happens in the story? Just tell me the story.”
When
She does not know one word in the story.
Tell her the meaning, act it out, then let her read it again.
When
She writes the answer with no unit.
“9 what? 9 elephants?” Make it funny.
When
She chooses the wrong sign.
Act it out with toys. The toys will show the answer.

Game놀이

Game · Story dice

You need: two dice

Roll two dice. Lia makes a story with the two numbers. She chooses add or take away.
You solve it. Then swap.
Extra: Lia must use one word from the word list, like ‘altogether’ or ‘difference’.

In the workbook

Eight mixed story problems. Answers are on the answers page.

Teaching Guide · Bonds to 10 and fact families · 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 · Bonds to 10 and fact families · liabooks.com/study

이 세트의 단어

add — put numbers together
altogether — all of them together
bar model — a picture with bars for the whole and the parts
bond (number bond) — two numbers that make a number
compare — look at two numbers to see which is bigger
count on / count back — count forward (+) or backward (−) from a number
counter — a small round thing for counting
difference — how much bigger one number is than another
digit — one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
double — the same number added twice
equals ( = ) — is the same as
fact family — 4 facts with the same 3 numbers
fewer / less — a smaller number
left — still here after some go
make 10 — use a bond to 10 to help add
minus ( − ) — the sign for subtract
missing number — the number in the empty box
more than — a bigger number by this much
number line — a line with numbers in order
number sentence — numbers and signs that make a fact
ones — single units; the right digit in a 2-digit number
part / whole — parts put together make the whole
partition — split a number into parts
pattern — something that repeats or changes in a regular way
place value — a digit's value depends on its place
plus ( + ) — the sign for add
related facts — facts connected to each other
subtract — take a number away
sum — the answer when we add
take away — remove some
tens — groups of ten; the left digit in a 2-digit number
ten frame — a box with 10 spaces
total — the number of all of them together
true / false — right / not right

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

On one page

Part	Topic	The big idea in one line	Key words	Workbook
C	Maths words	Many words mean + and many words mean −.	total, altogether, left, difference	My Maths Words, More Maths Words, Word Detective
Part 1	Bonds to 10	7 and 3 make 10.	bond, make 10, how many more	Bonds to 10
Part 2	Fact families	9, 4, 13 → four facts.	whole, part, fact family	Fact families
Part 3	Related facts	3 + 4 = 7, so 30 + 40 = 70.	ones, tens	Related facts
Part 4	Bonds to 100	4 + 6 = 10, so 40 + 60 = 100.	bond to 100, tens	Bonds to 100
Part 5	Add and subtract 1s	34 + 3 = 37. Only the ones change.	ones digit, tens digit	Add and subtract 1s
Part 6–7	Make 10 · Stories	8 + 5 = 8 + 2 + 3 = 13. Find the word, then the sign.	partition, then	Add by making 10, Story Problems, How did I do?

CTopicMaths wordsThe big idea in one lineMany words mean + and many words mean −.Key wordstotal, altogether, left, differenceWorkbookMy Maths Words, More Maths Words, Word Detective
Part 1TopicBonds to 10The big idea in one line7 and 3 make 10.Key wordsbond, make 10, how many moreWorkbookBonds to 10
Part 2TopicFact familiesThe big idea in one line9, 4, 13 → four facts.Key wordswhole, part, fact familyWorkbookFact families
Part 3TopicRelated factsThe big idea in one line3 + 4 = 7, so 30 + 40 = 70.Key wordsones, tensWorkbookRelated facts
Part 4TopicBonds to 100The big idea in one line4 + 6 = 10, so 40 + 60 = 100.Key wordsbond to 100, tensWorkbookBonds to 100
Part 5TopicAdd and subtract 1sThe big idea in one line34 + 3 = 37. Only the ones change.Key wordsones digit, tens digitWorkbookAdd and subtract 1s
Part 6–7TopicMake 10 · StoriesThe big idea in one line8 + 5 = 8 + 2 + 3 = 13. Find the word, then the sign.Key wordspartition, thenWorkbookAdd by making 10, Story Problems, How did I do?

Every day, ask these three questions

Question 1
“How do you know?”
Question 2
“Can you say it another way?”
Question 3
“Which word helped you?”

Next in class

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

What is in this guide

How to use this guide

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

Five golden rules

On one page

Every day, ask these three questions

Next in class

Small steps

Objects → pictures → numbers

Three kinds of question

Full sentences

Words the school uses

1. Ten frame

2. Part–whole model

3. Bar model

4. Tens and ones (base 10)

5. Number line

The big idea핵심

Words that mean add ( + )

Words that mean subtract ( − )

Tricky words — read this carefully

Teach it, step by step단계별 수업

Read the word pages together (workbook: My Maths Words and More Maths Words)

Same maths, different words

Word detective (workbook: Word Detective)

Ways to ask “add or subtract?”표현

Good questions to ask좋은 질문

If Lia is stuck막힐 때

Games (2)놀이

The big idea핵심

Get ready준비물

Teach it, step by step단계별 수업

Fingers warm-up

Ten frame

The hiding game

Find all the bonds, and the pattern

From adding to taking away

Other ways to ask the same question다른 표현

Good questions to ask좋은 질문

If Lia is stuck막힐 때

Games (2)놀이

Extra challenge더 도전

The big idea핵심

Get ready준비물

Teach it, step by step단계별 수업

Make the whole and the parts

Two adding facts

Two taking-away facts

Why we start with the whole

Write the family

Other ways to say it다른 표현

Good questions to ask좋은 질문

If Lia is stuck막힐 때

Games (2)놀이

Extra challenge더 도전

The big idea핵심

Get ready준비물

Teach it, step by step단계별 수업

Things, not only numbers

Show with tens

Use money

Taking away tens

Spot the mistake

Say the numbers clearly

Other ways to say it다른 표현

Good questions to ask좋은 질문

If Lia is stuck막힐 때

Game놀이

Extra challenge더 도전

The big idea핵심

Get ready준비물

Teach it, step by step단계별 수업

How many tens make 100?

Fingers are tens

Money

Taking away from 100

Other ways to say it다른 표현

Good questions to ask좋은 질문

If Lia is stuck막힐 때

Game놀이