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Teaching Guide — Bonds to 10 and fact families

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.

1394

Made with the help of AI. It follows the White Rose Maths Year 2 scheme (Autumn Block 2, steps 1–6), which many schools in England use. It is home practice, not official school material. If the school teaches something in a different way, follow the school.

What is in this guide

How to use this guide

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

PartWhat it is for
The big ideaThe one thing Lia must understand. Read this first. If you understand it, you can explain it in many ways.
Get readyThings to put on the table before you start: coins, Lego, paper, a pencil.
Teach it, step by stepA small lesson in 3–5 steps. You lines are things you can say. Child lines are answers your child might give. Do lines tell you what to do with your hands.
Other ways to say itThe same question in different English. Use many of them. Lia will hear all of them at school.
Good questions to askQuestions that make Lia think and explain. The school wants children to explain, not only to answer.
If Lia is stuckCommon mistakes and what to say.
GameA short game with no paper. Good for the car, the dinner table or bedtime.
Extra challengeHarder 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. Child lines are answers your child 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)

TimeWhat to do
2 minutesWarm up. Count together, or play one quick game from this guide.
5 minutesTeach the big idea with objects (coins, Lego, fingers). Use the “Teach it” steps.
8–10 minutesWorkbook. Let Lia work. Sit next to her. Ask questions. Do not give the answer too fast.
2 minutesTalk. “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.
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 a Year 2 maths lesson, so you can teach in the same way at home.

Small steps

Many schools in England use 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:

StageWhat it meansExample: 7 + 3
ConcreteReal things you can touch and move.7 red Lego bricks and 3 blue Lego bricks. Count them all: 10.
PictorialA drawing of the things.A ten frame with 7 dots and 3 dots.
AbstractOnly 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

KindWhat it asksExample
FluencyCan you do it quickly and correctly?“What is 6 + 4?”
ReasoningCan you explain why? Is it true or false?“Bo says 20 + 50 = 700. Is he right? How do you know?”
Problem solvingCan 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“Bo 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 saysNotWhy it matters
mathsmathBritish English, as used in schools in England.
ones and tensunitsWhite Rose says “ones”. Older books say “units”.
number sentenceequation (in Year 2)“4 + 6 = 10” is a number sentence.
subtract, minus, take away—subtract and minus are names for −. take away is for when some go. 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, as used in schools in England.
  • 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.
  • subtract, minus, take awayNot—Why it matterssubtract and minus are names for −. take away is for when some go. 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 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

1394
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 subtract one part from the whole, we get the other part.”

3. Bar model

169?
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 subtract 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 10p coins make £1.

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

8910111213+2+3
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?”
CHILD10!
YOU“Good. Now jump forward 3 more. Where are you?”
CHILD13.
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 · Bonds to 10 and fact families · liabooks.com/study
Start · Workbook pages 2–4

Maths words: what happens in the story?이야기 속 수학 영어 — 무슨 일이 일어나나

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

한국어 요약

이야기 문제에 나오는 영어 낱말을 낱말별 부호가 아니라 이야기 상황(더 온다·덜어 낸다·두 부분을 합친다·가른다·견준다)으로 묶어 정리했어요. gives, more, left처럼 같은 낱말이 다른 상황에 쓰이는 예, 식을 읽는 수학 말(add, plus, subtract, minus), 무슨 일이 일어나는지 묻는 질문과 놀이를 담았어요.

A story problem does not show the sign. One word cannot tell us the sign either. “Her friend gives her 5 more” — she has more at the end. “He gives 7 to Finn” — he has fewer. So we do not hunt for one magic word. We ask: What happens in the story? Do more come? Do some go? Are two parts put together? Are two groups compared? Lia pictures it first. Then she chooses the sign and checks that the answer fits the story.

What happensPicture itExample storyThe maths
Add more — more come, so there are more at the endStart with a group. Bring more in.There are 3 birds. 2 more birds come. How many birds are there now?3 + 2 = 5
Take away — some go, so there are fewer at the endStart with a group. Cover some, or push them away.There are 8 apples. Finn eats 3. How many apples are left?8 − 3 = 5
Put together — two parts make one wholeTwo groups side by side. Draw one ring round both.Dev has 5 big pens and 3 small pens. How many pens has he got?5 + 3 = 8
Split — we know the whole and one partDraw the whole. Ring the part you know.There are 8 pens. 5 are big. The rest are small. How many are small?8 − 5 = 3 or 5 + ? = 8
Compare — two groups, nothing comes or goesTwo rows. Match them up. Look at the ones with no partner.Dev has 12 cards. Omar has 8 cards. How many more cards does Dev have?12 − 8 = 4 or 8 + ? = 12
  • Add more — more come, so there are more at the endPicture itStart with a group. Bring more in.Example storyThere are 3 birds. 2 more birds come. How many birds are there now?The maths3 + 2 = 5
  • Take away — some go, so there are fewer at the endPicture itStart with a group. Cover some, or push them away.Example storyThere are 8 apples. Finn eats 3. How many apples are left?The maths8 − 3 = 5
  • Put together — two parts make one wholePicture itTwo groups side by side. Draw one ring round both.Example storyDev has 5 big pens and 3 small pens. How many pens has he got?The maths5 + 3 = 8
  • Split — we know the whole and one partPicture itDraw the whole. Ring the part you know.Example storyThere are 8 pens. 5 are big. The rest are small. How many are small?The maths8 − 5 = 3 or 5 + ? = 8
  • Compare — two groups, nothing comes or goesPicture itTwo rows. Match them up. Look at the ones with no partner.Example storyDev has 12 cards. Omar has 8 cards. How many more cards does Dev have?The maths12 − 8 = 4 or 8 + ? = 12
What happensWords you often hear
Add moremore come, get on, put in, gives her, buys
Take awayfly away, eat, pop, give away, get off, spend, lose, left, take away
Put togetheraltogether, total, in all, and
Splitthe rest, the others, how many are not …
Comparedifference, more than, fewer than, less than, how many more
  • Add moreWords you often hearmore come, get on, put in, gives her, buys
  • Take awayWords you often hearfly away, eat, pop, give away, get off, spend, lose, left, take away
  • Put togetherWords you often hearaltogether, total, in all, and
  • SplitWords you often hearthe rest, the others, how many are not …
  • CompareWords you often heardifference, more than, fewer than, less than, how many more
Clues, not rules

These words are clues about the story. They do not choose the sign. The same word can be in a different kind of story (see Tricky words below). Always ask “What happens?” first.

WordWhat it meansExample sentence
addput numbers togetherAdd 3 to 5. / 5 add 3 is 8.
plusthe name of the + sign5 plus 3 equals 8.
and … maketwo parts make a whole5 and 3 make 8.
sumthe answer when we addThe sum of 5 and 3 is 8.
more thana bigger number by this much3 more than 5 is 8.
subtractfind what is left, or find a missing partSubtract 3 from 8. (Start with 8!)
minusthe name of the − sign8 minus 3 equals 5.
fewer than / less thana smaller number by this much3 fewer than 8 is 5. 3 less than 8 is 5.
differencehow far apart two numbers areThe difference between 8 and 5 is 3.
equalsis the same as5 + 3 equals 8.
increase / decreasemake bigger / make smallerIncrease 5 by 3. (You will see these later.)
  • 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.
  • 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.
  • subtractWhat it meansfind what is left, or find a missing partExample sentenceSubtract 3 from 8. (Start with 8!)
  • minusWhat it meansthe name of the − signExample sentence8 minus 3 equals 5.
  • 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.
  • equalsWhat it meansis the same asExample sentence5 + 3 equals 8.
  • increase / decreaseWhat it meansmake bigger / make smallerExample sentenceIncrease 5 by 3. (You will see these later.)
Tricky wordWhy it is trickyHow to explain it
more“Mum puts in 5 more” — more come (+). But “How many more does Dev have than Omar?” — nothing comes. We compare two groups (12 − 8, or 8 + ? = 12).Ask: “Do more come? Or are we comparing two groups?”
gives“Omar gives 7 to Finn” — Omar has fewer (−). “Finn gives Omar 5” — Omar has more (+).Ask: “Who gets the things? Does Omar have more or fewer at the end?”
now“How many now?” comes after more come, and after some go.Ask: “What happened before now? Did some come, or did some go?”
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.”
differenceIn 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.”
sumIn 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 / lessTeachers 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.
leftLeft is also a direction (left and right). And “left” can be in an add story too: “Dev has 7 sweets left. Mum gives him 4 more.”“Left here means: still here, not gone.”
take awayAt school children may hear “take away” for any −.Use “take away” when some go. For numbers, say “subtract” or “minus”.
  • moreWhy it is tricky“Mum puts in 5 more” — more come (+). But “How many more does Dev have than Omar?” — nothing comes. We compare two groups (12 − 8, or 8 + ? = 12).How to explain itAsk: “Do more come? Or are we comparing two groups?”
  • givesWhy it is tricky“Omar gives 7 to Finn” — Omar has fewer (−). “Finn gives Omar 5” — Omar has more (+).How to explain itAsk: “Who gets the things? Does Omar have more or fewer at the end?”
  • nowWhy it is tricky“How many now?” comes after more come, and after some go.How to explain itAsk: “What happened before now? Did some come, or did some go?”
  • 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). And “left” can be in an add story too: “Dev has 7 sweets left. Mum gives him 4 more.”How to explain it“Left here means: still here, not gone.”
  • take awayWhy it is trickyAt school children may hear “take away” for any −.How to explain itUse “take away” when some go. For numbers, say “subtract” or “minus”.
YOU 부모가 할 말CHILD 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“Read this story card. What happens? Do more come, do some go, or do we compare?”
YOU“Can you show me with toys?”

Same maths, different words

YOU“Look: 5 + 3 = 8. How many ways can we say it?”
CHILD5 add 3 is 8. 5 plus 3 equals 8…
YOU“Great! Can you say it with the word sum? With the word more?”
YOU“Now let's do 8 − 3 = 5. Can you say it with minus? Can you tell me a story for it?”

Story detective (workbook: Story Detective)

YOU“I will tell you a tiny story. Picture it.”
YOU“There are 8 birds on a wall. 3 birds fly away. How many are there now?”
YOU“What happens in the story?”
CHILDSome birds fly away. So there are fewer.
YOU“Yes! Is it add or take away?”
CHILDTake away. 8 − 3 = 5.
YOU“How do you know?”
CHILDI know because some birds went away.
  • “What happens in the story?”
  • “Do more come, or do some go?”
  • “Are we putting two groups together?”
  • “Are we comparing two groups?”
  • “Will there be more or fewer at the end?”
  • “Can you show me with toys?”
  • “Is it plus or minus?”
  • “What happens in the story? How do you know?”

    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 that the answer fits the story.

  • “Can you make a sentence with the word ‘altogether’?”

    Note

    Using a word is harder than reading it.

  • 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 sees a word like ‘more’ or ‘gives’ and chooses the sign straight away.

    Say: “Let’s picture it first.” Act it out. “Who has more at the end? Who has fewer?”

  • 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.”

Game · Thumbs up, thumbs down

You need: nothing

  1. You tell a tiny story, for example “There are 6 birds. 4 birds fly away.”
  2. Lia shows thumbs up if there are more at the end, and thumbs down if there are fewer.
  3. She says what happened: “Some birds flew away, so there are fewer.”
  4. Use one word in two stories: “Mum gives you 2 more.” / “You give 2 away.”
  5. Swap: Lia tells a story, you show the thumb.
Game · Word hunt

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

  1. Look for maths words in real life: more, less, total, left, altogether.
  2. When Lia finds one, she reads the sentence and tells you what happens: do things come, go, join, or get compared?
  3. Supermarket receipts are great: they always have a “TOTAL”. Ask: “What does the total put together?”
In the workbook

Word pages and the Story Detective page.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study
Part 1 · Step 1 · Workbook pages 5–6

Bonds to 1010 모으기와 가르기

Two numbers that make 10.

한국어 요약

모아서 10이 되는 두 수(number bonds to 10)를 영어로 가르치는 법이에요. 한국 1학년의 10 모으기와 가르기, 10이 되는 더하기와 같은 내용이에요. 손가락과 수판(ten frame), 숨기기 놀이로 시작하는 대본, 같은 질문을 다르게 묻는 영어 표현, 막힐 때 할 말을 담았어요. 함께 보는 영상(약 4분)과 이어져요.

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
Watch together

Start with the video Number bonds to 10 (about 4 minutes). Watch it with your child. When Dad in the video asks a question, wait. Let your child answer before Lia in the video does. At a ‘Pause here’ card, pause and ask the question on the card. Then play the hiding game below with a real cup.

  • 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!
YOU 부모가 할 말CHILD 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?”
CHILD7.
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?”
CHILD7.
YOU“How many empty spaces?”
CHILD3.
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?”
CHILD6!
YOU“How do you know?”
CHILDBecause 4 and 6 make 10.
YOU“Let's check!”
DOLift the cup. Put them all back in the ten frame.
YOU“Is it full?”

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?”
CHILDThis number goes up and that number goes down.
YOU“Yes! 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?”
CHILD7.
YOU“And 10 − 7?”
CHILD3.
YOU“Good. Bonds help us take away too.”
태블릿으로 연습The same game is on screen: The Hiding Game.
  • “What goes with 7 to make 10?”
  • “7 and what make 10?”
  • “How many more to make 10?”
  • “What is the bond to 10 for 7?”
  • “7 plus what equals 10?”
  • “What do I add to 7 to get 10?”
  • “10 take away 7 is?”
  • “I have 7. I need 10. How many more do I need?”
  • “What is the missing number? 7 + ? = 10”
  • “How do you know?”

    Good answers

    “Because 7 and 3 make 10.” / “I looked at 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.

  • When

    Lia counts from 1 every time.

    That is fine at first. Then say: “Don't count the counters. Look at the empty spaces. How many?” Later: “Can you just know it?”

  • When

    She says 6 + 3 = 10.

    Use fingers: “Show me 6. Now 3 more. How many fingers are down?” Or put 6 and 3 in the ten frame: “Is it full?” 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.”

Game · Bond ping-pong

You need: nothing

  1. You say a number from 0 to 10: “Four!”
  2. Lia says the partner as fast as she can: “Six!”
  3. Then Lia says a number and you answer. Make a funny mistake sometimes, like Dad in the video. Can she catch you?
Game · Make 10 card game

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

  1. Put 12 cards face up.
  2. 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.
  3. A 10 card can be taken alone: “10 plus 0 equals 10.”
  4. Add new cards. The player with the most pairs wins.
  • 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, cup puzzles (‘Is Dev right?’), missing numbers, all the bonds to 10, and three short stories with pictures.

Later, for practice

Think with Lia: How many more to make 10? (about 3 minutes). In the video, Lia solves three story problems.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study
Part 2 · Step 2 · Workbook pages 7–8

Fact families덧셈과 뺄셈의 관계

Three numbers, four facts.

한국어 요약

세 수로 덧셈식 둘과 뺄셈식 둘을 만드는 덧셈과 뺄셈의 관계(fact family)를 영어로 가르치는 법이에요. whole과 part라는 말, 뺄셈은 늘 전체(whole)에서 시작한다는 점을 작은 물건과 part-whole 그림(전체를 두 부분으로 가른 그림)으로 보여 줘요.

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).

1394
whole 13, parts 9 and 4
1394
the same family as a bar model
  • 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
YOU 부모가 할 말CHILD 아이가 할 만한 대답DO 손으로 할 일

Make the whole and the parts

DOPut 9 counters of one colour and 4 of the other in the whole circle.
YOU“How many altogether?”
CHILD13.
YOU“This is the whole. The whole is 13.”
DOMove the 9 to one part circle and the 4 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…?”
CHILD13 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.
YOU“What is left?”
CHILD9.
YOU“So 13 − 4 = 9. Now start again and take away the 9. What is left?”
CHILD4.
YOU“So 13 − 9 = 4.”

Why we start with the whole

YOU“Can we do 4 − 13?”
CHILDNo…
YOU“In Year 2 we always start with the whole, the biggest number. The whole goes first when we subtract.”

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?”
CHILD13, the whole.
  • “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?”
  • “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.

  • When

    She writes 4 − 13 = 9.

    Point to the part–whole model. “Where do we start when we subtract? 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.

Game · Fact family houses

You need: paper and pens

  1. Draw a house. Write the whole (for example 12) in the roof.
  2. Draw two doors with the parts (7 and 5).
  3. Draw four windows. Lia writes one fact in each window.
  4. 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

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

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
  • Lego towers of 10 (or bundles of 10 straws or ice-cream sticks)
  • Some single bricks
  • Coins: 10p coins are perfect. Each one is a ten.
YOU 부모가 할 말CHILD 아이가 할 만한 대답DO 손으로 할 일

Things, not only numbers

YOU“3 apples and 4 apples make…?”
CHILD7 apples.
YOU“3 cars and 4 cars make…?”
CHILD7 cars.
YOU“3 tens and 4 tens make…?”
CHILD7 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?”
CHILD3 tens.
YOU“3 tens is 30. Let's count: 10, 20, 30.”
DOAdd 4 more towers.
YOU“Now how many tens?”
CHILD7 tens.
YOU“7 tens is 70. So 30 + 40 = 70.”

Use money

DOShow three 10p coins and four 10p coins.
YOU“How much money is this?”
CHILD70p.
YOU“3 coins and 4 coins make 7 coins. Each coin is 10p. So 30p + 40p = 70p.”

Taking away tens

YOU“8 − 3 = 5. So 80 − 30 = …?”
CHILD50.
YOU“How do you know?”
CHILD8 tens take away 3 tens is 5 tens. 5 tens is 50.

Spot the mistake

YOU“Omar says 20 + 50 = 700. Is he right?”
CHILDNo!
YOU“Why not?”
CHILD2 tens and 5 tens make 7 tens. 7 tens is 70, not 700.

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

Teen numberTens numberHow to hear the difference
13 thirTEEN30 THIRtyTeen numbers are strong at the end. Tens numbers are strong at the start.
14 fourTEEN40 FORtySpelling: forty has no u (not fourty).
15 fifTEEN50 FIFty
16 sixTEEN60 SIXty
17 sevenTEEN70 SEVenty
18 eighTEEN80 EIGHty
19 nineTEEN90 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
  • “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.”
  • “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.

  • 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.

Game · Tens shop

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

  1. Lia is the shopkeeper. You buy two toys: “I want the 30p car and the 40p ball. How much is that altogether?”
  2. Lia uses the small fact: 3 + 4 = 7, so 70p.
  3. Give her 90p: “How much change?” (90 − 70 = 20). Swap roles.
  • 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 page 10

Bonds to 100몇십과 몇십으로 100 만들기

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 10p 동전으로 1파운드(£1)를 만드는 놀이를 담았어요.

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).

10101010101010101010
4 tens and 6 tens make 10 tens = 100
  • 10 towers of 10 Lego bricks (or 10 bundles of straws)
  • Ten 10p coins, and a £1 coin to compare
  • Your ten fingers (each finger can be a ten!)
YOU 부모가 할 말CHILD 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?”
CHILD10.
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?”
CHILD4 tens are down. 6 tens are up.
YOU“4 tens is 40. 6 tens is 60. 40 and 60 make 100.”

Money

DOShow ten 10p coins.
YOU“Ten 10p coins make 100p. 100p is £1.”
YOU“I have 70p. How much more do I need to make £1?”
CHILD30p.
YOU“How do you know?”
CHILD7 and 3 make 10, so 70 and 30 make 100.

Taking away from 100

YOU“If 40 + 60 = 100, what is 100 − 60?”
CHILD40.
YOU“And 100 − 40?”
CHILD60.
  • “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?”
  • “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?”

  • 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?”

Game · Race to £1

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

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

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
  • 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!
YOU 부모가 할 말CHILD 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?”
CHILD3 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?”
CHILDThe ones.
YOU“How many ones now?”
CHILD7.
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?”
CHILD3.
YOU“Did the tens change?”
CHILDNo.
YOU“So 58 − 5 = 53.”

Look for the pattern

YOU“41 + 1 = 42. 41 + 2 = 43. 41 + 3 = 44.”
YOU“What do you notice?”
CHILDThe 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?”
CHILD89.
YOU“How did you do it?”
CHILD2 add 7 is 9, and the 8 tens stay.
  • “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.”
  • “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.

  • 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.

Game · Number spy

You need: nothing

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

You need: one dice, paper

  1. Start at 21. Roll the dice and add: 21 + 4 = 25. Write it.
  2. Keep going while the ones stay 9 or less. If a roll would pass 10, the other player takes the turn.
  3. Talk about the rule: “Which rolls can we use when we are at 25?” (1, 2, 3, 4)
  • 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 12–13

Add by making 1010을 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. 수판(ten frame), Rekenrek(구슬 계산기), 수직선, 수 묶기 네 가지 그림으로 보여 주고, 아이가 찾은 다른 방법도 인정해 주는 말을 담았어요.

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.

In class, Lia may see this on ten frames, on a rekenrek (a bead frame), on a number line, or with a number bond. The idea is always the same: make 10 first.

fill the first ten frame, then put the rest in the second
8910111213+2+3
jump to 10, then jump the rest
push 8, then 2 more to fill the top row, then 3 on the bottom row
523
split 5 into 2 and 3: 8 + 2 = 10, then 10 + 3
  • Two ten frames (two egg boxes, or draw two grids)
  • About 20 counters in two colours
  • A number line 0–20 (a ruler works)
  • A rekenrek — or make one: two strings with 10 beads on each (5 beads of one colour, 5 of another), or draw two rows of 10 circles on paper
YOU 부모가 할 말CHILD 아이가 할 만한 대답DO 손으로 할 일

Two ten frames

DOPut 8 counters in the first ten frame. Put 5 of the other colour next to it.
YOU“How many more does the first ten frame need to be full?”
CHILD2.
DOMove 2 of the 5 into the first frame.
YOU“Now the first frame is 10. How many counters are left outside?”
CHILD3.
YOU“10 and 3 make 13. So 8 + 5 = 13.”

Rekenrek

DOShow 9 + 5 on the rekenrek. Push 9 beads on the top row.
YOU“Look at the colours. 5 of one colour and 4 of the other. How many do you need to push to get to 10?”
CHILD1. 9 and 1 make 10.
DOPush 1 more bead. The top row is full.
YOU“How many more do you need to push to find the answer?”
CHILD4. I split 5 into 1 and 4.
DOPush 4 beads on the bottom row.
YOU“10 and 4 make 14. So 9 + 5 = 14.”

On a rekenrek the beads change colour after 5. A full row is 5 + 5 = 10, so Lia can see 5 and 10 at a glance, without counting the beads one by one.

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?”
CHILD9 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?”
CHILD2.
YOU“We need to jump 5 altogether. We jumped 2. How many more?”
CHILD3. So we land on 13.
YOU“Now 9 + 5. Put your finger on 9. Where do we jump first?”
CHILDTo 10. That is a jump of 1.
YOU“Fill in the jumps: +1, then +4. Write +1 above the first jump and +4 above the second.”
YOU“Now complete the workings: 9 + 1 + 4 = 14.”

“Complete the workings” means: write every step of your thinking, not only the answer.

Split with a number bond

DODraw a part-whole model. Write the smaller number, 7, in the whole (the top circle).
YOU“We have 8 + 7. Which number needs help to make 10?”
CHILD8. It needs 2.
YOU“So split 7 into 2 and 5. Write 2 and 5 in the two parts.”
DOCircle 8 + 2 in the working. That is your 10.
YOU“8 + 2 = 10. Then 10 + 5 = 15. So 8 + 7 = 15.”

Keep the bigger number and split the smaller one. Use bonds to 10 to find the two parts. Here the whole is 7, the number we split. It is not the answer, 15.

Other ways are OK too

YOU“Did anyone do it a different way?”
CHILDI 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.

  • “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.”
  • “Push the beads.”
  • “How many do you need to push to get to 10?”
  • “How many more do you need to push?”
  • “Fill in the jumps.”
  • “Complete the workings.”
  • “Use bonds to 10.”
  • “Can you find another way?”
  • “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.

  • “Why do the beads change colour after 5 on the rekenrek?”

    Good answers

    “So I can see 5 and 10 without counting.”

  • 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 counts the rekenrek beads one by one.

    Point at the colours. “One colour is 5. Both colours together make 10. How many of the other colour are on this side?”

  • 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?”

Game · Fill the frames

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

  1. Each player rolls and puts that many counters in their ten frames. Always fill the first frame before the second.
  2. Say your total the ‘make 10’ way: “I had 8, I rolled 5. 2 fill my frame, 3 more. I have 13.”
  3. The first player to fill both frames (20) wins.
  • Make 10 with bigger numbers: 28 + 5 = 28 + 2 + 3 = 33. (This is the next step — Part 7!)
  • 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, a rekenrek, number lines and number bonds. Then quick questions and a crayon story.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study
Part 7 · Step 8 · Workbook page 14

Add to the next 10 and across a 10다음 10의 배수까지, 10 넘어 더하기

48 + 5 = 48 + 2 + 3 = 53.

한국어 요약

10, 20, 30처럼 꽉 찬 10만 있는 수를 영어로 'multiple of 10'(10의 배수, 한국 1학년의 몇십)이라고 하는 것과, 주어진 수 다음의 10의 배수 찾기(46 다음은 50)를 가르쳐요. 그다음 48 + 5처럼 두 자리 수에 한 자리 수를 더할 때 다음 10의 배수까지 먼저 가고 남은 수를 더하는 방법을 수판, 수직선, 십 모형으로 보여 줘요.

A multiple of 10 is a number we say when we count in tens from 0: 10, 20, 30 … 100. It is made of full tens and zero ones. That is why it ends in 0. 46 is not a multiple of 10: it has 4 tens and 6 ones.

The next multiple of 10 after 46 is 50. It is the next full ten, not the next number (47). 46 is between 40 and 50. If a number is already a multiple of 10, the next one is 10 more: after 60 comes 70.

This helps with bigger adding. For 48 + 5: the next multiple of 10 is 50. 48 needs 2 more. So split 5 into 2 and 3. 48 + 2 = 50. Then 50 + 3 = 53. The 2 ones and the 8 ones make a new ten. This is Part 6 (make 10) with bigger numbers.

27 + 3 = 30: three full frames, zero ones
404650
46 is between 40 and 50. The next multiple of 10 is 50.
+
48 + 5: 2 ones fill the ten, then 3 more
484950515253+2+3
jump to the next multiple of 10, then jump the rest
  • Ten frames (draw a few grids of 2 × 5) and about 30 counters
  • Base 10 blocks — or make them: bundles of 10 straws with a rubber band, and single straws
  • A number line 0–100, or a ruler
YOU 부모가 할 말CHILD 아이가 할 만한 대답DO 손으로 할 일

Fill the frames

DOPut 17 counters in ten frames: one full frame and 7 in the next.
YOU“Add 3. How many now?”
CHILD20. Two frames are full.
DODo the same with 27 + 3.
YOU“What do you notice?”
CHILDEvery frame is full. There are zero ones.
YOU“10, 20 and 30 are called multiples of 10.”

Let Lia see and say it first. Give the name after.

The next multiple of 10

DOPoint to 46 on the number line.
YOU“What is the next multiple of 10 after 46?”
CHILD50.
YOU“How do you know?”
CHILD46 is between 40 and 50. 50 is the next full ten.
YOU“What about 60? What is the next multiple of 10 after 60?”
CHILD70. 60 is already a multiple of 10.

Add across a 10

DOShow 48 with base 10 blocks: 4 tens and 8 ones. Put 5 ones to the side.
YOU“We add 5. What is the next multiple of 10?”
CHILD50. 48 needs 2 more.
YOU“So split 5 into 2 and 3.”
DOMove 2 ones. Now there are 10 ones: swap them for a ten.
YOU“Now we have 5 tens. Add the 3 ones.”
CHILD53. 5 tens and 3 ones.

The moment 10 ones become one ten is the key idea. Let Lia do the swap herself.

How many to the next 10?

YOU“72 + □ = 80. What is the missing number?”
CHILD8.
YOU“How do you know?”
CHILD2 + 8 = 10, so 72 + 8 = 80.

Look at the ones. A bond to 10 gives the answer.

  • “What is the next multiple of 10?”
  • “What is the next full ten?”
  • “Which two multiples of 10 is it between?”
  • “How many to the next 10?”
  • “Add to the next 10, then add the rest.”
  • “Ten ones make a new ten.”
  • “Split the 5 into 2 and 3.”
  • “Add across a 10.”
  • “Is 46 a multiple of 10? How do you know?”

    Good answers

    “No. It has 6 ones.”

  • “What is the next multiple of 10 after 95?”

    Note

    100. Ten tens make 100.

  • “Why is 47 not the next multiple of 10 after 46?”

    Good answers

    “47 is the next number. It still has ones.”

  • “Can you do 36 + 7 by going to 40 first?”

    Note

    36 needs 4: split 7 into 4 and 3. 40 + 3 = 43.

  • When

    She says the next number: “After 46 comes 47.”

    “47 is the next number. Is it a full ten? Show me with ten frames.” Fill the frame to 50.

  • When

    She goes back: “The next multiple of 10 after 21 is 20.”

    “20 is before 21. Next means after.” Point to 20, 21 and 30 on the number line.

  • When

    She loses the new ten: 36 + 7 = 33.

    “6 and 7 make 13 ones. 13 ones are one ten and 3 ones. Where does the ten go?” Swap 10 cubes for a ten.

Game · Next ten, please!

You need: a number line 0–100 (or a ruler), or nothing at all

  1. One player says a number up to 99: “64.”
  2. The other says the next multiple of 10 and how many to get there: “70. 6 more.”
  3. Check together with a bond to 10 (4 + 6 = 10). Then swap.
  • The previous multiple of 10: before 46 comes 40.
  • Two steps across 100: 97 + 5 = 97 + 3 + 2 = 102.
  • Take away to a multiple of 10: 53 − 3 = 50. Then 53 − 5 = 53 − 3 − 2 = 48.
In the workbook

Find the next multiple of 10, add across a 10 with base 10 blocks, missing numbers and a cupcake story.

Teaching Guide · Bonds to 10 and fact families · liabooks.com/study
Part 8 · Workbook page 15

Story problems이야기 문제(문장제)

Read, picture it, say what happens, write the number sentence, check.

한국어 요약

영어 이야기 문제를 읽고, 그려 보고, 이야기에서 무슨 일이 일어나는지(더 온다·덜어 낸다·합친다·견준다) 말한 뒤 식을 세우고, 답이 이야기에 맞는지 확인하는 다섯 단계 순서를 가르쳐요. gives, rest, more처럼 같은 낱말이 다른 상황에 쓰이는 예와 아이가 직접 이야기를 만드는 문장 틀도 담았어요.

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.

StepWhat Lia doesWhat you can say
1. ReadRead the whole story. Then read it again.“Read it two times. The second time, read slowly.”
2. Picture itImagine it, act it out with toys, or draw a ten frame (a full ten and some more) or a bar model.“Can you show me with toys?”
3. What happens?Say what happens: more come, some go, two parts make a whole, or two groups are compared.“What happens in the story? Are there more or fewer at the end?”
4. Write a number sentenceChoose + or − from what happens, and write it: 16 − 7 = ?“Can you write it as a number sentence?”
5. Answer and checkSay the answer with the thing: “Omar has 9 stickers left.” Check that it fits the story.“9 what? Can Omar have more than 16 now?”
  • 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 ten frame (a full ten and some more) or a bar model.What you can say“Can you show me with toys?”
  • 3. What happens?What Lia doesSay what happens: more come, some go, two parts make a whole, or two groups are compared.What you can say“What happens in the story? Are there more or fewer at the end?”
  • 4. Write a number sentenceWhat Lia doesChoose + or − from what happens, and write it: 16 − 7 = ?What you can say“Can you write it as a number sentence?”
  • 5. Answer and checkWhat Lia doesSay the answer with the thing: “Omar has 9 stickers left.” Check that it fits the story.What you can say“9 what? Can Omar have more than 16 now?”
YOU 부모가 할 말CHILD 아이가 할 만한 대답DO 손으로 할 일

“Omar has 16 stickers. He gives 7 stickers to Finn. How many stickers does Omar have left?”

Read and picture

YOU“Let's read it two times.”
YOU“What is happening in the story?”
CHILDOmar gives stickers to Finn.
YOU“Does Omar have more stickers at the end, or fewer?”
CHILDFewer.

What happens?

YOU“Show me with toys. What happens to Omar’s stickers?”
CHILDSome go to Finn. So Omar has fewer.
YOU“Yes! Some go away, and we want to know how many are still with Omar. Is that add or take away?”
CHILDTake away.

Number sentence

YOU“What do we start with?”
CHILD16.
YOU“What do we take away?”
CHILD7.
YOU“Can you write the number sentence?”
CHILD16 − 7 = 9.

Answer and check

YOU“Say the answer in a full sentence.”
CHILDOmar has 9 stickers left.
YOU“Does 9 fit the story?”
CHILDYes. He gave some away, so 9 is less than 16.
YOU“Let's check. 9 + 7 = 16. Yes! That's our fact family.”
StoryWhy it is trickyThe maths
Her friend gives her 5 more.“Gives”, but Yuki gets more. More come.+
He gives 7 to Finn.Omar has fewer. Some go.−
5 are small. The rest are big.Nothing goes. “The rest” is the other part.11 − 5 or 5 + ? = 11 (a missing part)
How many more does Dev have than Omar?“More”, but nothing comes. We compare two groups.12 − 8 or 8 + ? = 12 (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.Picture the bus. Are there more or fewer people now?fewer people: − · more people: +
  • Her friend gives her 5 more.Why it is tricky“Gives”, but Yuki gets more. More come.The maths+
  • He gives 7 to Finn.Why it is trickyOmar has fewer. Some go.The maths−
  • 5 are small. The rest are big.Why it is trickyNothing goes. “The rest” is the other part.The maths11 − 5 or 5 + ? = 11 (a missing part)
  • How many more does Dev have than Omar?Why it is tricky“More”, but nothing comes. We compare two groups.The maths12 − 8 or 8 + ? = 12 (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 trickyPicture the bus. Are there more or fewer people now?The mathsfewer people: − · more people: +

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

FrameExample
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 biscuits. She gave 4 away. How many are left?
___ has ___ ___. ___ has ___ ___. How many do they have altogether?Yuki has 5 shells. Finn has 4 shells. How many do they have altogether?
___ has ___. ___ has ___. What is the difference?Dev has 12 pencils. Omar 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 biscuits. She gave 4 away. How many are left?
  • ___ has ___ ___. ___ has ___ ___. How many do they have altogether?ExampleYuki has 5 shells. Finn has 4 shells. How many do they have altogether?
  • ___ has ___. ___ has ___. What is the difference?ExampleDev has 12 pencils. Omar has 8 pencils. What is the difference?
  • “There are 10 spoons. We use 8. How many spoons are left?”
  • “You had 8 grapes. You ate 3. How many are left?”
  • “This bag has 30p. That bag has 40p. 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?”
  • “What is happening in the story?”

    Note

    Understanding first, numbers later.

  • “Will the answer be bigger or smaller than 16?”

    Note

    A quick check that the answer fits the story.

  • “Can you draw it?”

    Note

    A bar model or small circles is enough.

  • “Does your answer make sense?”

    Note

    If Omar gave stickers away, he can't have more than 16.

  • “Can you make up a story for 13 − 5?”

  • 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.

Game · Story dice

You need: two dice

  1. Roll two dice. Lia makes a story with the two numbers. She chooses what happens: do more come, or do some go?
  2. You solve it. Then swap.
  3. 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 C

Everyday English for maths time수학 시간 생활 영어

Useful sentences for giving instructions, praising and helping.

Starting and giving instructions

SayIt 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.
Picture it. What happens?Picture the story, then say what happens
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
  • Picture it. What happens?It meansPicture the story, then say what happens
  • 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.

  • “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

  • “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

  • “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 stemExample
___ 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 Omar 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 Omar 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.

SayIt 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
  • “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
Maths words

Words in this set이 세트의 단어

  • add — put numbers together
  • altogether — all of them together
  • bar model — a picture with bars for the whole and the parts
  • bead — a small round thing with a hole, on a rekenrek
  • 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
  • multiple of 10 — a number we say when we count in tens from 0: full tens, zero ones
  • 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
  • push — move something along with your hand
  • rekenrek — a frame with two rows of 10 beads; 5 beads are one colour and 5 are another
  • 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
  • workings — the steps you write to show how you found the answer
Teaching Guide · Bonds to 10 and fact families · liabooks.com/study

On one page

Put this on the fridge.

PartTopicThe big idea in one lineWords to learnWorkbook
StartMaths wordsAsk what happens: more come, some go, put together, or compare.total, altogether, left, differenceMy Maths Words, More Maths Words, Story Detective
Part 1Bonds to 107 and 3 make 10.bond, make 10, how many moreBonds to 10
Part 2Fact families9, 4, 13 → four facts.whole, part, fact familyFact families
Part 3Related facts3 + 4 = 7, so 30 + 40 = 70.ones, tensRelated facts
Part 4Bonds to 1004 + 6 = 10, so 40 + 60 = 100.bond to 100, tensBonds to 100
Part 5Add and subtract 1s34 + 3 = 37. Only the ones change.ones digit, tens digitAdd and subtract 1s
Part 6Add by making 108 + 5 = 8 + 2 + 3 = 13.partition, thenAdd by making 10
Part 7Next multiple of 1048 + 5 = 48 + 2 + 3 = 53.multiple of 10, new tenAdd across a 10
Part 8StoriesPicture the story, then choose the sign.altogether, leftStory Problems, How did I do?
  • StartTopicMaths wordsThe big idea in one lineAsk what happens: more come, some go, put together, or compare.Words to learntotal, altogether, left, differenceWorkbookMy Maths Words, More Maths Words, Story Detective
  • Part 1TopicBonds to 10The big idea in one line7 and 3 make 10.Words to learnbond, make 10, how many moreWorkbookBonds to 10
  • Part 2TopicFact familiesThe big idea in one line9, 4, 13 → four facts.Words to learnwhole, part, fact familyWorkbookFact families
  • Part 3TopicRelated factsThe big idea in one line3 + 4 = 7, so 30 + 40 = 70.Words to learnones, tensWorkbookRelated facts
  • Part 4TopicBonds to 100The big idea in one line4 + 6 = 10, so 40 + 60 = 100.Words to learnbond to 100, tensWorkbookBonds to 100
  • Part 5TopicAdd and subtract 1sThe big idea in one line34 + 3 = 37. Only the ones change.Words to learnones digit, tens digitWorkbookAdd and subtract 1s
  • Part 6TopicAdd by making 10The big idea in one line8 + 5 = 8 + 2 + 3 = 13.Words to learnpartition, thenWorkbookAdd by making 10
  • Part 7TopicNext multiple of 10The big idea in one line48 + 5 = 48 + 2 + 3 = 53.Words to learnmultiple of 10, new tenWorkbookAdd across a 10
  • Part 8TopicStoriesThe big idea in one linePicture the story, then choose the sign.Words to learnaltogether, leftWorkbookStory 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

    “What happens in the story?”

Next in class

After these steps, children usually subtract across 10 (for example 42 − 6), add and subtract tens, and then add and subtract two 2-digit numbers. Bonds to 10, making 10 and the next multiple of 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