OuiSi · Math

Two cards, one equation

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Grades 3–5 Teaching 35 min Plus 3 to set out, 3 to clear Class any size Set any Prep paper for working

set out 3′ Two numbers, and a rule 8′ Build the equation 12′ Swap and argue 10′ Close 5′ clear 3′

Goal: Children build an equation from two photographs, solve each other's, and argue about what was being counted — because two correct answers usually means two different definitions.
Materials: One OuiSi Photo-Card set, about eight cards per pair. Paper and pencils.

Grade 3: Two cards, one sign. Add multiplication once addition is quick, and skip the order question.
Grade 4: Add the order question, then three cards and two signs in step 2.
Grade 5: Division and remainders — and what the leftover actually is in the photograph.
All three: The full 35 minutes. What changes here is the difficulty, not the length.

1 · Two numbers, and a rule

8 min

Pairs, about eight cards face up.

Find two cards where you can count something on each. Write both numbers down.

Then the step that matters more than the counting.

Write down your counting rule. What counted as one thing, and what did you leave out?

Half-hidden objects, things at the edge, things out of focus. Writing the rule down now is what makes the disagreement in step three productive instead of circular.

2 · Build the equation

12 min

Put a sign between your two numbers, work out the answer, and write the whole thing down — both numbers, the sign, the equals, and the answer.

The whole thing. Six times four is half a sentence, six times four equals twenty-four is the equation.

Once pairs have one, change the operation rather than the numbers.

Same two cards. Now multiply.

Six groups of four — where is that in either photograph?

It is in neither, and that is the question. Six leaves and four stones are not six groups of four of anything. The arithmetic is fine and the meaning has to be invented, so have them invent one — six baskets of four stones, four shelves of six jars. Building the situation that fits the sum is the real work.

Then the order question.

Swap to a minus, or a divide. Does the order matter now? Which card has to go first?

3 · Swap and argue

10 min

Pairs swap cards only. Papers stay face down — no numbers, no rule, no equation.

Count their two cards yourselves. Write your numbers and your own counting rule.

Only now do the papers come up.

Compare. Did you get the same two numbers? If not, read each other's rule and find where they differ.

Hand over the numbers and a pair will do the arithmetic without ever looking at the photographs. They have to count it themselves for the disagreement to be real. Both pairs are usually right under their own rule, so the argument is about definitions rather than arithmetic.

If the numbers match, ask them to find a card where their two rules would have disagreed.

Whose rule would you use if you had to agree on one? Why that one?

4 · Close

5 min

Which was harder — building the equation or agreeing what was in the picture?

Watch for

Skipping the counting rule. Step one's second half is what makes step three work. Without it the argument is just two people insisting.
Treating a disagreement as an error. Both pairs are usually right. Say so, then ask which rule is more useful.
Claiming the product is in the picture. It is not, and saying so is the honest move. The sum is correct and the situation that would make it mean something has to be invented — that invention is the task, not a consolation prize.
Remainders brushed aside. In grade 5, a remainder is the interesting part — what is actually left over in the photograph?

Adapt

Grade 4 and up — three cards, two signs, and ask what changes if you work left to right instead.
Grade 5 remainders — four cards among three baskets leaves one over. Ask what the leftover is, not just that there is one.
Children who think faster than they write — let them state the equation aloud while a partner writes it.
Number anxiety — choose cards with small quantities. The argument in step three needs no large numbers.
Multilingual learners — numerals and signs carry it. The counting rule can be drawn rather than written.
Extension — build an equation whose answer is a number you found in a third card.

Curriculum links. Counting two quantities and recording the counting rule used · Writing a complete equation — both numbers, sign, equals, answer · Applying multiplication and division to a pictured quantity · Testing whether order matters for an operation · Resolving a disagreement by comparing definitions.
Standard codes vary by state and district — these are the skills exercised, for you to map to your own.

For grades K–2 see Two cards, one sum, which builds the same idea with counters that stay on the cards.
Screen-free. No codes and no devices. Works with any OuiSi Photo-Card set.