Activity 01
Pairs: Grid Paper Multiplication
Students draw decimals on grid paper, shading sections to represent values like 0.4 as four tenths. They overlay grids to multiply, count shaded unit squares for the product, and place the decimal accordingly. Partners explain their shading to confirm the rule.
Justify the placement of the decimal point in a product of two decimals.
Facilitation TipDuring Grid Paper Multiplication, circulate and ask pairs to articulate how they counted decimal places after computing the whole-number product.
What to look forProvide students with two problems: 1) Calculate 2.7 x 0.4 and explain how you determined the decimal place in your answer. 2) Calculate 15.6 ÷ 3 and explain how you placed the decimal point in your answer.
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Activity 02
Small Groups: Decimal Shop Challenge
Set up a class shop with decimal-priced items. Groups receive a budget and shopping list, perform divisions to check affordability, and multiply costs for totals. Rotate buyer and cashier roles, then share strategies for decimal divisions.
Compare dividing a decimal by a whole number to dividing a whole number by a decimal.
Facilitation TipIn the Decimal Shop Challenge, listen for students explaining why dividing by a decimal less than one increases the quotient, using their bar models as evidence.
What to look forWrite 'Multiply 3.14 by 100' on the board. Ask students to write down the answer and hold up their whiteboards. Then, ask 'What is 12.5 divided by 0.5?' and have them show their answers.
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Activity 03
Whole Class: Power of 10 Relay
Call students to board one by one. Display a decimal; first shifts for ×10, next for ×100, passing a marker. Class verifies with place value charts. Correct sequence wins points; discuss predictions.
Predict the effect of multiplying a decimal by a power of 10.
Facilitation TipFor the Power of 10 Relay, pause after each round to ask students to predict the next step before moving sliders, reinforcing rightward movement of the decimal.
What to look forPresent two division problems: 4.8 ÷ 2 and 4.8 ÷ 0.2. Ask students to work in pairs to solve both. Then, lead a class discussion: 'What was different about solving these two problems? How did changing the divisor from a whole number to a decimal affect your steps and the answer?'
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Activity 04
Pairs: Division Error Hunt
Provide cards with decimal division problems and incorrect workings. Pairs identify errors, like misplaced decimals in 4.5 ÷ 1.5, correct them, and rewrite steps. Share one fix with class.
Justify the placement of the decimal point in a product of two decimals.
What to look forProvide students with two problems: 1) Calculate 2.7 x 0.4 and explain how you determined the decimal place in your answer. 2) Calculate 15.6 ÷ 3 and explain how you placed the decimal point in your answer.
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Generate Complete Lesson→A few notes on teaching this unit
Teach decimal multiplication by first ignoring the decimal to build confidence in whole-number computation, then layering in decimal placement through repeated practice and peer explanation. Avoid rushing to rules—instead, rely on grids and models to reveal patterns. Research shows that students who manipulate visual tools before formalizing steps retain understanding longer and make fewer persistent errors.
Students will confidently multiply and divide decimals by whole numbers and other decimals, explaining their process and justifying decimal placement in products and quotients. They will compare cases, predict outcomes with powers of 10, and correct common errors through discussion and peer feedback.
Watch Out for These Misconceptions
During Grid Paper Multiplication, watch for students who only count decimal places from one factor and ignore the other.
Have pairs recount the total decimal places from both factors before placing the decimal point, using the grid squares to physically mark the places. Ask them to justify their count to their partner before writing the final product.
During the Decimal Shop Challenge, watch for students who believe dividing by a decimal less than one gives a smaller answer.
Prompt students to use their bar models to partition a whole into equal parts (e.g., 5 ÷ 0.5 becomes 5 wholes divided into 5 groups of 1). Ask them to compare the size of each part to the whole and explain why there are more parts when dividing by a fraction.
During the Power of 10 Relay, watch for students who move the decimal point left when multiplying by 10^n.
Pause the relay and have students trace the movement of digits with their fingers on the slider. Ask them to verbalize, 'Multiplying by 10 shifts digits right, so the decimal must move right too.' Repeat with 100 and 0.1 to reinforce the pattern.
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