Decimal Operations Start

Overview

In this first lesson of the unit “Decoding Decimals and Fractions,” students begin multiplying and dividing multi-digit decimals using area models, number lines, and base-ten manipulatives. They will connect decimal operations to place value and explain what the answers mean.

Learning intentions

• Students will be able to model multiplication of a decimal by a whole number using visual representations.
• Students will be able to model division of a decimal by a whole number using repeated grouping and sharing models.
• Students will explain, in words, how place value changes when multiplying and dividing decimals.
• Students will check reasonableness of answers using estimation strategies.

Success criteria

• I can show a decimal multiplication using a place-value model (e.g., area or base-ten blocks).
• I can solve a division question with a decimal answer using a visual model and explain the steps.
• I can justify where the decimal point in my answer comes from.
• I can estimate and decide if my final answer makes sense.

Curriculum links

• Number Sense and Operations: operations with decimals (including multiplication and division) connected to place value.
• Understanding and applying strategies for computing with decimals, and interpreting results in context.
• Mathematical reasoning and communication: describing thinking using models and language.

Lesson structure (30 minutes)

1. 0–3 min: Launch with a visual prompt Show two grids/area models labelled in tenths and hundredths (e.g., 0.3 and 2.4). Ask: “If each small square is one tenth (or one hundredth), how many tenths/hundredths are there altogether?” Students share quick observations about place value.

2. 3–10 min: Multiply a decimal by a whole number (model first) Use base-ten blocks or an area model for the example: 0.6 × 4. Action: Build 0.6 as 6 tenths, then group into 4 equal sets (or enlarge the area by repeating). Record: 0.6 × 4 = 2.4. Teacher explicitly points out: “We’re counting tenths; multiplying by 4 gives tenths that can be regrouped into ones and tenths.”

3. 10–16 min: Guided practice (one more example, then connect to an algorithm) Do 1 guided example: 1.2 × 3 using an area model (12 tenths grouped into three sets). Target result: 3.6. Then show the place-value reasoning for the decimal point using estimation: “1.2 is about 1, so the answer should be about 3.” Discuss why 3.6 fits.

4. 16–22 min: Divide a decimal by a whole number (sharing/grouping model) Use sharing model with 2.4 ÷ 4. Show 2.4 as 24 tenths. Share into 4 equal groups: each group is 6 tenths, so 2.4 ÷ 4 = 0.6. Have the student label each group using tenths (and regroup into ones only if needed).

5. 22–27 min: Independent computation with checks Give two short tasks (teacher selects based on accuracy):

• Task A (multiplication): 0.8 × 5
• Task B (division): 3.0 ÷ 6 Student models one and computes the other, then estimates to check reasonableness (e.g., 0.8 is near 1, so 0.8×5 near 5). Teacher prompts for explanation: “Where did the decimal point come from?”

6. 27–30 min: Exit ticket—explain using one sentence Student writes (or orally states) an exit ticket response:

• “In decimals multiplication/division, the decimal point is placed by thinking about ____.” And one final answer with a quick check (estimate or model consistency).

Resources

• Base-ten blocks (tenths and hundredths) or place-value disks
• Centimetre-grid paper or printed area model templates for tenths/hundredths
• Decimal cards (e.g., 0.6, 1.2, 2.4) and whole-number cards (e.g., 3, 4, 5, 6)
• Whiteboard/markers or a digital equivalent
• Estimation reference cards (round to nearest whole or tenths)
• Worked example chart: “Model → Count place value → Regroup → Record”
• Exit ticket slips

Assessment

• Teacher observation during modelling: correct placement of tenths/hundredths in the visual representation.
• Accuracy of computed answers and the ability to justify the decimal point using place value language.
• Exit ticket: a clear sentence connecting decimal point placement to place value/regrouping.

Differentiation

• Support for struggling learners: provide a partially completed area/sharing model where the decimal point and regrouping are pre-marked; allow extra time to count tenths/ hundredths before computing.
• Support with visuals: use a “two-step” approach—first show the model, then compute; provide sentence frames like “I grouped ___ tenths into ___ equal parts, so each part is ___.”
• Extension for advanced learners: give a word problem such as “A ribbon is 1.5 m long. You cut it into 3 equal pieces. How long is each piece?” (Students must model division and interpret the unit length.)
• EAL/SEN: allow responses using diagrams and numbered steps; use consistent terms (tenths, ones) and repeat the same model structure for multiplication and division; offer simplified numbers first (tenths only) before introducing hundredths.

Extension (optional)

• Advanced word problems with context and multi-step reasoning:
• “A bottle holds 2.4 L. You pour 0.6 L into each container. How many full containers can you fill? Show your model.”
• “If 3.6 kg is shared equally among 9 people, how much does each person receive?” Students represent both multiplication/division with models, then explain how the operation matches the story situation.