Solve joining, separating, and comparing stories

Learning goal: Solve addition and subtraction stories within twenty with the unknown in different positions. Represent the actual relationship with objects, drawings and an equation containing a box for the unknown. Do not choose an operation merely because a story contains the word more or left; identify what is known and what the question asks.

Start with a joining story: eight children are at a table and five join them. The starting amount and change are known, but the result is unknown. Draw eight marks, then five more, and write 8 + 5 = □. The total is thirteen. Label every amount with the counted unit, children, so a mark does not become an unlabeled decoration.

Move the unknown. Eight children are at the table; some join; now there are thirteen. The equation is 8 + □ = 13, and the question asks how many joined. Count on from eight to thirteen or match the two groups to find five. If some children were there first, five joined and thirteen are now there, write □ + 5 = 13. The starting amount is eight. All three versions describe a joining relationship but ask for different amounts.

For taking-from stories, distinguish starting amount, removed amount and remainder. With fourteen counters and six removed, 14 − 6 = □ asks for the remaining eight. In 14 − □ = 8, the removed part is unknown. In □ − 6 = 8, the starting amount is unknown. Act out the complete story and check the result by rebuilding the starting collection.

Putting-together and taking-apart stories can concern parts present at the same time rather than a change over time. Seven red beads and four blue beads make eleven beads. If eleven beads include seven red beads, four are blue. The total and two parts remain the relevant quantities even when nobody arrives or leaves.

Comparison asks how much greater or smaller one amount is than another. If one group has twelve cards and another has nine, align nine pairs and observe three unmatched cards. The difference is three cards. If a group has three more than a group of nine, the larger amount is twelve; if twelve is three more than another amount, that smaller amount is nine. The comparison diagram shows two aligned groups, and the difference counts unmatched objects rather than the entire longer group.

Worked example 1: Unknown change. A box contains six blocks and later contains fifteen after blocks are added. Draw six known blocks and continue adding until fifteen. Nine were added, so 6 + 9 = 15. The answer is not fifteen because the question asks for the change.

Worked example 2: Unknown start. A child gives away four stickers and has seven left. Rebuild the earlier amount by joining four given-away stickers with seven remaining stickers. Eleven were present at first: 11 − 4 = 7. Check both the story and the equation.

Worked example 3: Compare without moving objects. Ana has ten cards and Bo has six. Pair six from each group. Ana’s four unpaired cards show the difference: ten is four more than six. Neither child has to give cards away for a subtraction comparison to be useful.

Guided practice: Rewrite one joining and one taking-from story three ways so the start, change and result are each unknown in turn. Use counters to justify the equations. Next describe part-part-total and comparison situations, including a larger amount, smaller amount and difference unknown in separate examples. Keep all quantities within twenty.

Independent evidence: Solve the varied practice problems below and create a drawing for each. Write an equation with a box in the position representing the actual unknown before filling it. Ask a partner to retell the situation from the drawing. Repeat across days with all situation types; one result-unknown addition example does not establish this broad target.

Scoring and feedback: Award separate credit for a correct relationship/model, equation and answer with its unit. If a learner always places the box after the equal sign, compare two versions of the same story and point to the information that changed. If the comparison answer is the larger total, return to matched and unmatched objects. Check an unknown starting amount by acting out the whole story again.