Multiplication Arrays and Facts

Overview

Students review addition and subtraction (including regrouping) and then learn multiplication as groups and arrays. The lesson moves from concrete models (equal groups, repeated addition) to visual representations (arrays, number lines, skip counting) and finally to short equations and one-step word problems.

Learning intentions

• Students will be able to solve addition and subtraction review problems using drawings, number lines, and regrouping strategies when needed.
• Students will be able to represent multiplication as equal groups and arrays.
• Students will be able to use repeated addition and skip counting to find products for 0–12 multiplication facts.
• Students will be able to solve simple one-step multiplication word problems using an equation with a missing factor.

Success criteria

• I can solve addition and subtraction problems and explain my strategy using a model or number line.
• I can show 3×4 using an array, equal groups, repeated addition, and skip counting.
• I can write a multiplication equation that matches my model (with the unknown represented by a blank or box).
• I can use a fact strategy (counting by 1s/2s/5s/10s, or known fact families) to find products of two one-digit numbers up to 12.

Curriculum links

• Operations and Algebraic Thinking: Interpret products as total objects in equal groups.
• Operations and Algebraic Thinking: Use multiplication and division within 100 with strategies and fact recall.
• Operations and Algebraic Thinking: Solve word problems with drawings and equations including a symbol for the unknown.
• Operations and Algebraic Thinking: Use multiplication facts of two one-digit numbers from memory by the end of Grade 3 (building toward fluency in 3–6).

Lesson structure (30 minutes)

1. 0–5 min · Warm-up (Add/Sub Fluency). Teacher displays 6 short problems (3 addition, 3 subtraction; mix with/without regrouping). Students choose a strategy (hundreds chart, number line, or quick algorithm) and complete on mini-whiteboards; teacher circulates and checks accuracy and reasoning.

2. 5–10 min · Review task cards (Partner). Teacher assigns pairs a set of 4 task cards: addition word problem, subtraction word problem, and two computation cards. Students read, model (draw or use counters), then write an equation. Teacher listens for correct vocabulary: sum, difference, total, how many more/less.

3. 10–15 min · Explicit instruction: Equal groups to multiplication. Teacher shows counters in 3 equal groups of 4 (or 4 groups of 3 for differentiation) and asks: “How many altogether?” Teacher models: repeated addition (4+4+4), skip counting (4,8,12), and the array picture. Students complete a guided example with teacher:

• Model: 3 groups of 4
• Repeated addition: 4+4+4=12
• Multiplication: 3×4=12 Sentence stem: “I know 3×4=12 because…”

4. 15–20 min · Small-group center: Arrays & fact families (Rotate quickly). Teacher groups students into three levels and runs one center while others do brief independent practice (teacher-led mini-check).

• Beginner: arrays with 2× up to 5×, using grids and counting dots
• Intermediate: arrays up to 3×12 or 4×12 with skip counting support
• Advanced: include missing factor and fact family (e.g., 3×?=18, or 4×6=24 implies 6×4=24)

5. 20–26 min · Partner game: “Build, Match, Write.” (Manipulatives). Using a deck of cards, each pair: (a) builds the model with tiles/counters (or draws array), (b) matches it to an equation strip, (c) writes the multiplication equation and product. Game includes one subtraction/addition quick prompt tied to the story (e.g., “If you add 6 more groups…” or “How many were left after removing…”).

6. 26–30 min · Independent practice + Exit ticket. Students complete a short worksheet page (2 computation, 1 array-to-equation, 1 word problem). Exit ticket (1 problem) checks missing factor or simple one-step word problem. Teacher collects for progress monitoring.

Resources

• Counters, base-ten blocks or two-color chips, array mats (grid paper or laminated dot arrays)
• Number lines (0–50), skip-counting strips (by 2s, 3s, 4s, 5s, 10s)
• Fact-family cards (0–12) and sentence stem strips
• Task cards (add/sub review + simple word problems)
• Differentiated multiplication worksheets (3 levels) and answer keys
• Math journal or mini-whiteboards + markers
• Timer for rotations; timer cards for ADHD supports

Assessment

• Formative: warm-up mini-whiteboards (accuracy + method), teacher observation during partner modeling
• Formative: center checkpoint (students explain one model-to-equation connection with a stem)
• Exit ticket: missing factor or one-step multiplication word problem scored with a 0–2 rubric (0 incorrect, 1 partial/model present, 2 correct equation + product)

Differentiation

• Beginner support: large-print arrays; limited fact range (0–5); provide step-by-step example on desk; number line from 0; word problem with visuals and sentence frame (“There are ___ groups of ___.”)
• Intermediate support: fact range 0–12; partial product chart (blank boxes); use skip-counting line; require both repeated addition and multiplication equation.
• Advanced support: include missing factors (e.g., □×3=15, 4×□=28 with scaffolded number line) and fact family reasoning; ask for two representations (array + repeated addition) and justify with “because.”
• ADHD/Autism/OHI supports: clear routine, small chunks, movement allowed during center, visual schedule, frequent check-ins, reduce writing load (circling/matching) when needed, preferential seating, sensory tools (fidget during practice).
• Speech/Language supports: sentence stems and “choral response” during skip counting; allow pointing/first-draft oral responses before writing.

Printable worksheet set (use today)

Create one page per level (large print for Beginner). Include the same sections in the same order.

Section A: Addition/Subtraction Review (2 problems + 2 problems)

• Beginner: 18+7, 25−9, 34+20 (no regrouping), 45−30 (no regrouping)
• Intermediate: mix regrouping (e.g., 28+17, 45−18)
• Advanced: 2-digit + 2-digit with one regroup; add/sub word problem

Section B: Array/Equal Groups to Equation (2 problems)

• Provide pictures of arrays. Students write: repeated addition and multiplication equation. Example models:
• 2 rows of 6 (2×6)
• 5 groups of 3 (5×3)

Section C: Skip Counting / Missing Factor (1 problem)

• Beginner: fill in product (e.g., 3×4=__) using skip-counting strip
• Intermediate: missing factor from a model (e.g., □×3=12)
• Advanced: missing factor with two-step reasoning support (e.g., 4×□=20)

Section D: One-step Word Problem (1 problem)

• Beginner: “There are 3 bags. Each bag has 4 marbles. How many marbles?”
• Intermediate: “A teacher makes 6 equal rows of 2 stars. How many stars?”
• Advanced: include an extra detail distractor but require one multiplication (with visual highlight of equal groups)

Answer key (quick reference)

• Section B examples:
• 2×6 = 12; repeated addition 6+6=12
• 5×3 = 15; repeated addition 3+3+3+3+3=15
• Section D (sample):
• 3 groups of 4 → 3×4=12
• 6 rows of 2 → 6×2=12 (Use your generated models to match your worksheet pictures.)

Exit ticket (single problem)

“Draw an array for 4×3, then write the multiplication equation and product.”

• Beginner: allow drawing or counters; require 4×3=12
• Intermediate: require equation + repeated addition (3+3+3+3=12)
• Advanced: ask “Write the related fact: 3×4=__ too.”