Show addition and subtraction with real actions

Learning goal: Represent joining and taking-away situations with objects, drawings, spoken explanations and equations, and solve within ten. Work with an adult using large counters or toy animals. Kindergarten learners can explain and draw their thinking before they can independently write an equation; an adult can record the symbols.

Place three toy birds on a mat. Tell a complete story: “Three birds sit beside a pond. Two more birds arrive. How many birds are there now?” Keep the first three in place and add two. Count the combined group: one, two, three, four, five. Addition describes putting these parts together. Say “three and two make five,” then show 3 + 2 = 5. The plus sign connects the two amounts being joined. The equal sign says the two sides name the same total, not simply that an answer comes next. A drawing of this story need not show wings or beaks; circles are enough if they show the mathematics in the problem, three and two more. That rule applies wherever drawings are mentioned in the standards.

The illustrated part-part-total model names the two starting groups and the resulting total. Its final row shows five counters, not three counters followed by an unrelated numeral. Count the objects in every row and match them to the labels. The total is not an additional group to count along with the starting groups: it is another view of the same objects after joining.

For subtraction, start with seven counters and move two off the mat. Count the five that remain. Say “seven take away two leaves five,” and record 7 − 2 = 5. The seven names the amount before the action; two names the removed part; five names the remaining part. In a drawing, cross out removed objects so a reader can distinguish what was there from what remains. Do not count crossed-out objects as part of the answer to “How many are left?”

Other representations can show the same mathematics. Hold up four fingers and then one more, make two claps followed by three claps, or act out children joining a line. After every representation, ask what each number counts. A mental picture can help once the child understands the physical action. The goal is to connect the story, model and numbers rather than memorize a word that always means add or subtract: the relationship and the question determine the operation.

Worked example 1: Joining within ten. Four toy cars are parked. Three more arrive. Draw four circles in one color and three in another, but count all seven in the final group. Explain 4 + 3 = 7 by pointing to each part. If a learner answers three, that counts only the arriving cars; revisit what “now” asks about.

Worked example 2: Taking away. Nine blocks are on a shelf and four are used to build a tower elsewhere. Draw nine blocks and cross out four. Count the uncrossed blocks: five. Write 9 − 4 = 5. The question asks about the shelf, so do not count the tower blocks again.

Worked example 3: Find a missing part. Six cups are needed for snack. Four are already on the table. Put down four counters, then add one at a time until the total is six. Two were added, so two more cups are needed. Explain the result with a model; the missing amount is not necessarily the last number spoken in a count.

Guided practice: Tell one joining story and one taking-away story with totals no greater than ten. Have the child model the action, draw a record and say a complete answer with the object name. Then exchange roles so the child tells a story for an adult’s model.

Independent work: Solve 2 + 5, 8 − 3 and a story with four present and seven needed. For each, provide a picture or object demonstration and a sentence explaining what the numbers mean. Ask the learner to create a different story for 6 − 2. Accept objects, fingers, drawings or a clear mental explanation; notation alone is not required to demonstrate the concept.

Scoring and feedback: For each task, award one point for the correct result and one for a model or explanation matching the action. A correct numeral with an unrelated model needs follow-up. If a child counts removed objects, physically separate the removed and remaining sets and restate the question. Practice within five first if ten objects are difficult to track. Extend by showing the same story with two representations and asking why both have the same answer.