Multiplying by Six

Overview

In this lesson, students practice multiplying by 6 using interactive games, arrays, and collaborative strategies. They connect multiplication to division and use properties of operations to solve and check products.

Learning intentions

Students will be able to:

• interpret 6 × ___ as equal groups of 6 and describe what the product means
• multiply within 100 using strategies (fact patterns, properties of operations, and the relationship between multiplication and division)
• use properties of operations to find unknown facts (for example, breaking 6 × 7 into 6 × 5 and 6 × 2)
• use multiplication facts to solve division equations involving a missing whole number

Success criteria

• I can explain what 6 × 4 means using groups or an array.
• I can find 6 × 1 through 6 × 10 and say how I know.
• I can solve a related division equation using a multiplication fact.
• I can use a property of operations (like distributive property) to break apart a problem and recombine.

Curriculum links

• Operations and Algebraic Thinking: interpret products as equal groups (3.OA.A.1)
• Operations and Algebraic Thinking: determine unknown whole numbers in multiplication/division equations (3.OA.A.4)
• Operations and Algebraic Thinking: apply properties of operations to multiply and divide (3.OA.B.5)
• Operations and Algebraic Thinking: fluently multiply/divide within 100 and use strategies and relationships (3.OA.C.7)

Lesson structure (60 minutes)

1. 0–5 min · Quick Start (Fact Warm-Up). Teacher displays two “Think Fast” problems: 6 × 2 and 6 × 5; students answer and give a quick strategy (skip counting, array, or known facts).

2. 5–12 min · Teach: Meaning of 6×___ (Groups to Product). Teacher shows 6 objects in a circle labeled “1 group,” then repeats until 6 × 4 is shown; students record: “6 × 4 is ___ total objects” and sketch a simple array.

3. 12–23 min · Interactive Game 1: Array Race. Teacher sets up a timer and shows a card like “6 × 7”; students build a 6-by-7 array using counters or grid paper, then write the product. Teacher calls “switch strategies” halfway: students try to also compute using skip counting by 6 or a known fact (like 6 × 5).

4. 23–33 min · Collaborative Practice: Property Work Stations (Rotate). Teacher directs students through 3 short rounds (about 3 minutes each).

• Station A (Distributive): “6 × 7” is split into “6 × 5” and “6 × 2.” Students write the addition equation that matches.
• Station B (Commutative/Reciprocal): Students match “6 × 8 = ” with “ ÷ 6 = 8.”
• Station C (Check & Explain): Students pick one product and explain how they know using an array or repeated addition.

5. 33–45 min · Direct Practice: Multiply-by-6 Checklist. Teacher hands out 8–10 problems (range 6 × 1 to 6 × 10 plus one mixed fact like 6 × 9). Students complete, but must include a strategy label for at least 3 answers (skip counting, arrays, or distributive property).

6. 45–55 min · Division Connection: Missing Number Challenge. Teacher writes 3 equations on the board, each with a blank:

• 6 × 6 = ___
• ___ ÷ 6 = 7
• 6 × 4 = ___ and ___ ÷ 4 = 6 (students choose the correct missing value) Students solve using known products, then explain in one sentence how multiplication helped division.

7. 55–60 min · Exit Ticket (One Minute Demonstration). Students answer two items independently:

• Draw/describe what 6 × 5 means and write the product.
• Complete: 42 ÷ 6 = ___ and show the multiplication fact you used.

Resources

• Counter set or snap cubes (at least 60 total)
• Grid paper or place-value mats
• “Array Race” problem cards (6 × 1 to 6 × 10)
• Station cards for distributive, reciprocal (multiplication/division), and check & explain
• Student recording sheet: “My Strategy Was…”
• Whiteboard markers and an eraser
• Timer
• Exit ticket slips or one shared exit ticket sheet

Assessment

• Observe during Array Race: check that students correctly form equal groups/rows and record the correct product.
• Listen during Station rotations: confirm students explain using arrays, skip counting, or the distributive property.
• Exit ticket: verify accurate multiplication by 6 and correct division with missing values plus a connection to the multiplication fact.

Differentiation

• Support: provide a partially completed array for one example (for example, 6 × 4 already drawn with 2 rows) and sentence starters: “6 × 7 means ___ groups of 6” and “I used distributive property by splitting 7 into 5 and 2.”
• Support for division: give a fact anchor chart with 6 × 1 through 6 × 10; allow students to point to the product before filling the quotient blank.
• Extension: include one multi-step item such as “6 × 9 using 6 × 5 and 6 × 4” and ask students to write the distributive equation and the final product.
• EAL/SEN: allow verbal responses or drawing first, then copying the math; keep numbers consistent (no more than 1–10 for the multiplier) and reduce the station set to only two rotations if needed while still completing the exit ticket.