Math // Addition & Subtraction

What the equals sign means

Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false

Ages
6 to 7
Type
Concept
Builds on
1 topic
Leads to
3 topics
Standards
1 code

Quick check

Does the learner understand that '=' means 'the same as', so they can tell you whether '4 + 3 = 8 − 1' is true or false?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Explain that 6 = 6 is true because both sides are the same
  • Determine that 4 + 1 = 5 + 2 is false
  • Understand that = does not mean 'the answer comes next' — it means balance

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

1 topic
  • Reading +, −, and = symbolsRequired

    Addition & Subtraction // Ages 5 to 6

    Deep understanding of = requires already being able to read and write number sentences

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What the equals sign means

Ages 6 to 7 // Concept

Leads to

3 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 6–7, teach that the equals sign means 'is the same value as' / 'balances' — a statement of balance between two expressions, not an instruction to 'work out the answer'. Deliberately vary equation form (answer on the left like 8 = 5+3, operations on both sides like 5+2 = 6+1, bare identity like 8 = 8) and prioritise judging true/false and relational reasoning (compensation) over always computing both sides. A physical or on-screen balance model anchors equality as equilibrium rather than a finish line.

Common misconceptions

  • Reading '=' as 'work out the answer' / 'the total goes here' (operator misconception) — so 8 = 5+3 looks 'backwards' or wrong.
  • Rejecting bare identities like 8 = 8 as 'not a sum' or incomplete.
  • In a+b = c+□, writing the running total of the left side into the box (e.g. 8+4 = 12+□ → box = 12 or 12+? = to next), the classic Falkner/Carpenter error.
  • Believing there can only be one number after the '='.
  • Thinking both sides must LOOK identical rather than share a value.

Useful representations

  • Pan balance / balance beam with equal masses or cubes on each side
  • Number balance (bucket balance) where hanging weights on numbered pegs balance
  • Part-whole bar with the same total shown two ways
  • Double ten-frame showing both expressions holding equal counts
  • Equation cards in varied layouts with a true/false sorting mat

Teaching practices

  • Read '=' aloud consistently as 'is the same value as' / 'balances', never 'makes' or 'gives you'.
  • Present equations in varied, non-standard forms early (answer-left, operations-both-sides, identity) so children never fix on left-to-right computing.
  • Use a pan balance or balance-beam model so equality is felt as physical equilibrium, not a finish line.
  • Prioritise true/false judging and relational thinking (compensation: 5+2 = 6+1 because one more here, one less there) over always calculating both sides.
  • Include missing-number-in-any-position tasks (□ = 7−5, 8 = □+3) to force the relational reading.

Activities to try

  1. 1

    Balance beam: build both sides and watch it level

    Why it works: The equals sign is the pivot/balance point: two sides are equal when they share the same value, regardless of how each side looks or which side 'the answer' is on. '=' is not a direction to compute leftward.

    1. Set an expression on the left pan and another on the right (for example 5+2 on the left, 6+1 on the right) using identical cubes on a physical pan balance (5 cubes and 2 cubes on one side, 6 cubes and 1 cube on the other), or number/operation tiles on an on-screen balance that weighs each side by its value.
    2. Predict whether the beam will tip or settle level, and say why, before releasing it.
    3. Watch whether the beam tips or settles level: with identical cubes (or an on-screen balance that weighs by value), it sits level only when both sides share the same value.
    4. Try a case where the sides look different but balance: put 8 on the left and 5+3 on the right and observe that the beam still sits level.
    5. Try a missing-number challenge: add to one pan to level the beam, e.g. make 8+3 balance 9+□ (the blank is 2, since both sides then make 11).
  2. 2

    True or false across varied forms

    Why it works: A number sentence is true when both sides have the same value, in any layout — identity, answer-left, or operations on both sides — and relational reasoning can decide this without always calculating.

    1. Judge whether each sentence is true or false and say how you decided: 6 = 6; 7 = 8 − 1; 5 + 2 = 2 + 5; 4 + 1 = 5 + 2.
    2. Judge 4 + 1 = 5 and 5 = 4 + 1 (both true) and 4 + 1 = 6 (false).
    3. For 5 + 2 = 6 + 1, decide true or false WITHOUT fully computing both sides, using compensation (one more on one side, one less on the other).
    4. Sort a set of equation cards into 'balanced / true' and 'not balanced / false' piles.
    5. Fill a missing number to make the sentence true: 8 = □ + 3 (blank is 5); 8 + 3 = 9 + □ (blank is 2); □ = 7 − 5 (blank is 2).
  3. 3

    Static balance picture to anchor 'the same as'

    Why it works: Both sides of a true equation share one value even when they look different; a level balance pictures this meaning of '='.

    1. Look at a level balance with an expression on each pan (e.g. 8 on one side, 5+3 on the other).
    2. Tap or point to each side to reveal its value.
    3. Say why the balance stays level: 'both sides are 8, so they balance — that is what = means'.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
1.OA.7

Math // Addition & Subtraction

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