Joining Groups

Overview

In this 30-minute lesson, students model addition as joining two groups and finding the total. The lesson builds from familiar counting and sets, using concrete objects, movement, drawings, and equations to connect addition stories to mathematical representations.

Learning intentions

• Students will be able to model addition by joining two groups.
• Students will be able to count the total within 10.
• Students will be able to explain an addition story using objects, drawings, actions, or numbers.
• Students will be able to represent the same addition in more than one way.

Success criteria

• I can make two groups.
• I can join the groups together.
• I can count and state how many there are altogether.
• I can show my addition with objects, a drawing, or an equation.

Curriculum links

• Represent addition with objects, fingers, mental images, drawings, sounds, actions, explanations, expressions, or equations.
• Solve addition word problems within 10 using objects or drawings.
• Use addition to describe joining groups and finding a total.

Lesson structure (30 minutes)

1. 0–4 min · Hook and connect. Teacher opens with the introduction and joining-groups slides, showing two groups of classroom objects, such as 2 cubes and 3 cubes, and asks, “What happens when we join these groups?” Students act out joining two groups with their hands, predict the total, and share how they know.

2. 4–9 min · Model addition. Teacher models a simple story: “There are 2 bears. 3 more bears join them. How many bears are there now?” Using counters, the teacher makes two separate groups, slides them together, counts all the counters, and records 2 + 3 = 5 on the model-and-equation slide. Students repeat the language, “___ and ___ make ___ altogether,” while touching or moving each counter.

3. 9–16 min · Partner modeling. Teacher pairs the 10 students and gives each pair counters and a visual story mat. The teacher displays one joining story at a time on the partner-practice slides, such as “4 red cubes and 2 blue cubes are joined. How many cubes altogether?” Students build the two groups, physically join them, count the total, and explain their model to a partner. The teacher checks that students count the combined group rather than recounting only one part.

4. 16–22 min · Show it in different ways. Teacher demonstrates that the same addition can be acted out, built with counters, drawn, and written as an equation, using the four-representations slide. Students complete two examples on the addition representations worksheet by drawing or placing counters for each story and stating the total. Students who are ready add the matching equation; students working within 5 may use the smaller-number examples.

5. 22–27 min · Independent check and discussion. Teacher reads a final joining story from the final story and discussion slide: “Mia has 3 stickers. She gets 4 more stickers. How many stickers does she have altogether?” Students solve on the addition representations worksheet using objects, a drawing, or an equation. Invite several students to show different models and ask, “How does your representation show joining?”

6. 27–30 min · Exit ticket and recap. Teacher displays the recap slide and gives each student a quick oral or drawn exit prompt: “Show 2 and 1 joined together. How many altogether?” Students model, draw, or say the answer, then complete the sentence, “___ and ___ make ___.” Teacher closes by restating, “Addition can show groups joining to make a total.”

Resources

• the complete addition slide deck
• the addition representations worksheet
• Tactile counters or linking cubes
• Visual story mats with two joining spaces and one total space
• Large demonstration counters or magnetic objects
• Pencils, crayons, and clipboards
• Number cards 0–10
• Optional ten-frames
• Small work-area baskets for partner materials

Assessment

• During modeling, ask students to identify the two groups, the joining action, and the total; note whether they count all objects accurately.
• During partner work, listen for complete explanations such as “2 and 3 make 5 altogether” and check whether students can connect a story to a model.
• Use the final prompt as an exit check. Record whether each student can model joining and state the total independently, with support, or not yet.

Differentiation

• Support: Use counters, ten-frames, large visual story mats, gestures, and a number line. Offer numbers within 5, then move to totals within 10 when appropriate. Model one step at a time and provide the equation frame “___ + ___ = ___.”
• Language and dyslexia-friendly access: Read every story aloud, use clear pictures with minimal text, avoid requiring students to read the problem independently, and provide oral sentence frames: “I had ,” “ joined,” and “Now there are ___.” Let students answer by speaking, pointing, acting, drawing, or manipulating tactile counters.
• Special education supports: Pre-teach the words “join,” “more,” and “altogether.” Pair students intentionally, provide repeated practice with the same routine, and use hand-over-hand or guided counting only when needed. Offer frequent praise for representing the joining action, not just for giving the answer.
• Extension: Students represent one addition story with counters, a drawing, an oral explanation, and an equation. Invite advanced learners to find a different pair of groups that makes the same total within 10 and explain how the two equations are alike.