Build Two-Digit Products

Overview

Students use place value and equal groups to multiply a one-digit number by a two-digit number. They partition the two-digit factor into tens and ones, solve each part, and combine the partial products, building from familiar multiplication facts and addition strategies.

Learning intentions

• WALT represent a two-digit number as tens and ones.
• WALT multiply a one-digit number by each part of a two-digit number.
• WALT combine partial products to find the total.
• WALT explain our strategy using equations, materials, drawings, or words.

Success criteria

• I can partition a two-digit number into tens and ones.
• I can solve each smaller multiplication fact accurately.
• I can add my partial products to find the answer.
• I can show and explain how I know my answer is reasonable.

Curriculum links

• Mathematics and Statistics — multiplicative thinking, using equal groups and known multiplication facts.
• Mathematics and Statistics — place value, partitioning two-digit numbers into tens and ones.
• Mathematics and Statistics — representing, communicating, and justifying mathematical thinking.
• Mathsteasers — rich, higher-order mathematical questions that deepen understanding and provide appropriate challenge.

Lesson structure (29 minutes)

1. 0–4 min · Hook and connect. Teacher displays the opening problem from the multiplication introduction deck: “There are 4 trays with 23 apples in each. How many apples altogether?” Students estimate, turn and talk, and share a strategy without needing to calculate yet. Prompt: “What do you already know that could help?”

2. 4–9 min · Model partitioning. Teacher uses the next slides to represent (4 \times 23) as four groups of 2 tens and 3 ones, then records:

• (23 = 20 + 3)
• (4 \times 23 = (4 \times 20) + (4 \times 3))
• (80 + 12 = 92) Students draw or describe the groups and identify why the 20 and 3 are kept separate.

3. 9–13 min · Guided example. Teacher reveals (3 \times 14) on the multiplication introduction deck and asks students to solve it with a partner before discussing:

• (14 = 10 + 4)
• (3 \times 10 = 30)
• (3 \times 4 = 12)
• (30 + 12 = 42) Students explain the meaning of each line and use a quick estimate to check whether 42 is sensible.

4. 13–22 min · Independent and paired practice. Teacher distributes the partition-and-multiply practice sheet. Students solve the first two examples independently, then compare methods with a partner. The worksheet includes space for an array, equal-groups drawing, or partitioning equation. Suggested questions:

• (2 \times 13)
• (4 \times 21)
• (3 \times 32)
• (5 \times 14) Teacher circulates, checking that students multiply both the tens and ones and do not treat 23 as 2 + 3. Ask: “What does your 60 represent?” and “Where can I see the three ones in your model?”

5. 22–26 min · Reasoning challenge. Teacher displays the challenge from the multiplication introduction deck: “Mia says (3 \times 24 = 3 \times 20 + 4 = 64). Is Mia correct? Prove it.” Students discuss in pairs, identify the missing multiplication, and explain the correction: (3 \times 24 = 60 + 12 = 72). Invite one or two students to show a different representation.

6. 26–29 min · Plenary and exit check. Teacher shows the final prompt on the multiplication introduction deck and asks students to complete one response on the back of the worksheet: “Solve (2 \times 36). Show your partitioning and explain one step.” Students hand in the response as they leave. Teacher briefly revisits the learning intention and names the key idea: multiply the tens and ones, then combine the products.

Resources

• the multiplication introduction deck
• the partition-and-multiply practice sheet
• Mini-whiteboards and pens
• Tens-and-ones materials, such as place-value blocks or bundled straws
• Pencils and erasers
• Board or projector

Assessment

• Listen during partner talk for correct use of “tens”, “ones”, “equal groups”, “partial product”, and “altogether”.
• During worksheet practice, check whether students partition the two-digit number correctly and calculate both partial products.
• Use the exit response to identify students who are ready for less scaffolding and students who need further work with place value or basic multiplication facts.

Differentiation

• Support students with place-value blocks, a tens-and-ones drawing template, multiplication fact charts, and the sentence frame: “I partitioned ___ into ___ and ___. First I found ___. Then I found ___.”
• Work with a small group on (2\times) and (5\times) examples, using concrete equal groups before recording equations.
• Accept oral explanations, drawings, arrays, or materials as evidence of understanding, particularly for students with writing or language difficulties.
• Extend confident students by asking them to solve the same problem in two ways, create a true-or-false statement, or find two different one-digit-by-two-digit products that equal 72.