Multiplication as Addition

Overview

In this first lesson of the unit, students revisit multiplication as “groups of equal size,” connecting it directly to repeated addition. They will represent simple multiplication expressions with concrete/visual models and explain the relationship in their own words.

Learning intentions

Students will be able to:

• Write a multiplication expression to represent repeated equal groups.
• Represent a multiplication equation as repeated addition using pictures or objects.
• Explain why multiplication can be seen as repeated addition (equal groups).
• Interpret multiplication expressions without computing when the context is clear.

Success criteria

Students can:

• Correctly match a set of equal groups to a multiplication sentence (e.g., 3 groups of 4).
• Draw or build a model that shows repeated addition for a given multiplication sentence (e.g., 3×4 shown as 4+4+4).
• Use at least one sentence stem to explain the “why” (multiplication makes equal groups the same number of times).
• Tell what a multiplication expression means by describing the groups, without needing to calculate.

Curriculum links

• Operations and Algebraic Thinking — write simple expressions and interpret numerical expressions (understanding meaning without evaluating).
• Number and Operations in Base Ten — place value understanding supports the fluency students will use later (kept as a readiness connection for today’s models).
• Number and Operations in Base Ten — multiplication and division relationships will be revisited after students solidify multiplication meaning.
• Number and Operations—Fractions — model-based thinking for products supports later fraction multiplication units (readiness).

Lesson structure (30 minutes)

1. 0–3 min · Bell work. Teacher posts two quick prompts: “Show 3 groups of 5 using drawing or objects” and “Write an addition sentence for that situation.” Students answer on scrap paper; teacher circulates to note who uses groups accurately.

2. 3–8 min · Homework correction (rapid). Teacher reviews answers to last night’s practice (or teacher-provided warmup sheet) using 2–3 student examples: one correct group model, one partially correct model, one incorrect addition match. Students compare their work, correct one mistake, and write a brief “what I changed” note.

3. 8–15 min · Direct teach: equal groups. Teacher demonstrates with manipulatives (counters) arranged into equal rows (example: 3 rows of 4). Teacher asks: “How many counters in total?” then reframes: “Instead of counting everything each time, we can add the same number of counters—repeated addition.” Students watch, then complete a guided fill-in:

• Model: ___ groups of ___
• Repeated addition: ___ + ___ + ___
• Multiplication sentence: ___ × ___

4. 15–22 min · Guided practice: match representations. Teacher displays a small card set (no more than 4):

• A picture of equal groups (e.g., 4 groups of 3 dots)
• A repeated addition sentence (e.g., 3 + 3 + 3 + 3)
• A multiplication sentence (e.g., 4 × 3) Teacher models how to decide which representation matches. Students work in pairs to match and justify using sentence frames: “Because there are ___ groups of ___, we add ___ the same number of times.” Teacher calls on 2 pairs for quick explanations.

5. 22–28 min · Independent practice: represent and explain. Students choose (or are assigned) one problem:

• “Draw and write repeated addition for 2 × 6.”
• “Draw and write repeated addition for 5 × 2.” Students create a visual (array, rows, or dots) and write both the repeated addition and the multiplication sentence, plus one sentence explaining “why multiplication is repeated addition.”

6. 28–30 min · Exit ticket. Teacher collects a short prompt: “What does 3 × 4 mean? Write repeated addition and one sentence explaining why.” Students answer in 3–4 minutes.

Resources

• Counters or base-ten blocks (small sets for 10 students)
• Dot cards/picture cards showing equal groups
• Sentence starter strips (e.g., “3 × 4 means…”, “We use repeated addition because…”)
• Student recording sheets (model + addition + multiplication)
• Whiteboard or chart paper for teacher demonstration
• Timer for structured segments

Assessment

• Formative checks during bell work and circulation: look for correct “equal groups” structure.
• Observation during guided practice: students’ ability to justify the match between picture, addition, and multiplication.
• Exit ticket: verify repeated addition matches the multiplication expression and the explanation sentence includes “equal groups” or “same number added each time.”

Differentiation

• Support: Provide a partially drawn template (e.g., 3 rows with 4 blanks) and sentence frames for explanation (“There are ___ equal groups of ___.” “So we add ___ the same number of times.”).
• Support for students who struggle with drawing: allow manipulatives instead of pictures; require written repeated addition and multiplication sentence only.
• Extension: Give a challenge card: “Write two different repeated addition sentences that both represent the same multiplication expression” (e.g., show that order of addends doesn’t change the total, but group meaning stays consistent).
• EAL/SEN: Use consistent vocabulary (group, equal, each time, repeated). Offer a word bank with “groups,” “times,” “add,” “equal,” and “same.”

Learning outcomes for today (Lesson 1)

• Students will articulate that multiplication represents equal groups and can be expressed as repeated addition.
• Students will accurately represent a multiplication situation using a visual model and the matching repeated addition sentence.
• Students will interpret a multiplication expression by describing the groups it represents, without needing to evaluate the total.