Lambton Learning Hub Math ladder

Math · Rung 3 of 7

Addition and subtraction.

Taking away, finding the difference, and seeing that subtraction is addition read backwards.

Where this sits

  1. 1Counting and number sense
  2. 2AdditionBefore
  3. 3Addition and subtractionYou are here
  4. 4Place valueNext
  5. 5Adding, subtracting, multiplying
  6. 6All four operations
  7. 7Fractions, decimals, money

What this rung is

Subtraction means more than "take away". It is also the difference between two amounts (how many more does Sam have?) and the missing part (I have 3, I need 8, how many more?). Seeing that 8 − 3 asks "3 and what make 8?" turns every addition fact your child already knows into a subtraction fact.

The goal is adding and subtracting within 20 by a smart route. Bigger numbers, like 52 − 17, wait for the Place value rung.

Ready to start when your child…

  • Knows every pair that makes 10 without counting.
  • Adds within 20 without counting from one.
  • Reads "=" as "is the same as".
  • Can make up a story for an addition sum.

These are the "ready to move on" signs from Addition. If a few are missing, spend a little longer there.

The six steps inside this rung

Each step builds on the one before. Most children spend weeks on some steps and days on others.

  1. Taking away

    Start with real things and remove some. How many are left?

    7 apples, eat 2 → 5 left

  2. Counting back and counting up

    Count back for a small take-away. When the numbers are close, count up from the smaller one instead.

    12 − 9: "9 … 10, 11, 12. Three."

  3. Think addition

    Use an addition fact you already know to subtract.

    8 − 3: "3 and what make 8? 5."

  4. Fact families

    Three numbers make four facts.

    3 + 5 = 8, 5 + 3 = 8, 8 − 5 = 3, 8 − 3 = 5

  5. Back through ten

    Subtract down to 10 first, then take the rest.

    13 − 5 = 13 − 3 − 2 = 8

  6. Which one is it?

    Story problems where your child decides whether to add or subtract, including "how many more".

    "Sam has 9 stickers, Lee has 6. How many more does Sam have?"

Try it: hops on a number line

Tap "New take-away" or "New adding" for a problem. Your child works it out, then tap "Show the hops" to check.

Activities

Snack take-away

At home · Step 1

You need: Grapes, crackers or berries

Count out a small pile. Your child eats a few. How many are still on the plate? Say the subtraction sentence together.

“You had 9. You ate 4. How many are still on the plate?”

Bottle bowling

At home · Outside · Steps 1 and 4

You need: 10 empty plastic bottles, a ball

Set up 10 bottles and roll. How many fell? How many are standing? Write both facts: 10 − 4 = 6 and 4 + 6 = 10.

“4 fell down, so how many are standing?”

Fact family houses

At home · Step 4

You need: Paper and a pencil

Draw a house with three numbers in the roof, like 3, 5 and 8. Your child writes the four facts in the windows.

“Can you find all four facts that live in this house?”

Corner shop

At home · Step 6

You need: 20 counters or tokens, a few things with price tags up to 20

Your child has 20 tokens and buys one thing. How many tokens are left? Then: how many more would they need for something that costs more?

“You have 15 tokens and the apple costs 8. How many do you have left?”

Chalk back-hops

Outside · Steps 2 and 5

You need: Sidewalk chalk

Draw a line from 0 to 20. Stand on 13 and hop back 5, stopping at 10 on the way. Then try counting up: stand on 9, hop to 12.

“Three hops back to 10, then two more. Where are you?”

Rock collection compare

Outside · With a group · Step 6

You need: A bag each, a minute on a timer

Two children collect rocks for one minute, then line them up side by side. Who has more, and how many more?

“Your line is longer. How many more rocks do you have?”

Salute!

With a group · Steps 3–4

You need: A deck of cards with the face cards taken out (ace counts as 1)

Three players. Two each take a card and hold it to their forehead without looking. The third says the total. Each forehead player works out their own card from the total and the card they can see.

“The total is 13, and I can see a 6. So my card is …?”

Race to zero

With a group · Steps 2 and 5

You need: One die, paper for each player

Everyone starts at 20. Take turns rolling and subtracting. You must land on zero exactly to win; if a roll is bigger than your number, you miss that turn.

“You're on 7 and rolled 4. Where are you now?”

Common snags

Counting the start number when counting back

For 9 − 3 they say "9, 8, 7" and answer 7. Say the start number, then count back the three on fingers: "nine … eight, seven, six."

Taking the small number from the big one, whatever the story says

Act the story out with objects before writing anything.

Only knowing "take away"

Ask "how many more?" and "how far apart?" questions too, with two lines of objects side by side.

Hunting for keywords

"More" doesn't always mean add. Ask your child to picture or act out the story first.

Counting back a long way

For 14 − 12, counting up from 12 is just two steps. Show that both ways give the same answer.

Ready to move on when…

Tick them off as you see them. Saved on this device only.

Extras

  • From the library: Elevator Magic and Monster Musical Chairs, both by Stuart J. Murphy.
  • Free online: Number Line from the Math Learning Center, for drawing hops on screen.