Multiply by Ten

Overview

In lesson 3 of Place-Value Power Moves, students use place-value relationships to find 10 times a number and 1/10 of a number. They connect whole-number and decimal examples to the idea that a digit’s value becomes 10 times greater when it moves one place left and 1/10 as great when it moves one place right.

Learning intentions

• Students will be able to use a place-value chart to multiply or divide by 10.
• Students will be able to apply the relationship to whole numbers and decimals.
• Students will be able to explain how a digit’s position and value change.
• Students will be able to use whole-number exponents to recognize 10 as (10^1) when appropriate.

Success criteria

• I can move a digit one place in the correct direction on a place-value chart.
• I can accurately find 10 times a number or 1/10 of a number.
• I can explain one answer using a sentence frame.
• I can complete at least 80% of the practice accurately.

Curriculum links

• Number and Operations in Base Ten — place-value relationships in multi-digit numbers.
• Number and Operations in Base Ten — patterns when multiplying or dividing decimals by powers of 10.
• Number and Operations in Base Ten — reading and representing decimals to thousandths.
• Mathematical practice — reason abstractly, use place value, and explain thinking with equations and models.

Lesson structure (30 minutes)

1. 0–3 min · Error-analysis hook. Display on the error-analysis hook slide: “A student says the 6 in 600 is 10 times the 6 in 60 because 600 is larger. Do you agree?” Teacher asks students to identify and correct the error without calculators. Students silently decide, then turn and explain that the digit is in different places and has different values: 600 versus 60.

2. 3–8 min · Direct model. Using the place-value model slides, teacher builds 70 on a place-value chart with place-value disks, models 10 × 70 = 700, and then models 1/10 of 500 = 50 by moving each digit one place in the appropriate direction. Students track the movement with a finger or physical left/right motion and repeat: “Multiplying by 10 moves digits one place left; finding 1/10 moves digits one place right.”

3. 8–16 min · Guided practice. Teacher reveals one problem at a time on the guided-practice slides, pausing after each for students to predict, represent, and explain: 10 × 40, 1/10 of 800, 10 × 0.6, and 1/10 of 7. Students use place-value charts or disks, record equations, and show answers with verbal, pointing, or written responses. Teacher checks for the key misconception that the decimal point itself “moves”; emphasize that the digits change place and value.

4. 16–25 min · Partner or independent practice. Distribute the multiply-and-divide-by-ten practice sheet. Teacher assigns partners or individual work and provides the sentence frames: “___ is 10 times ___ because the digit moved ___ place(s) .” and “ is 1/10 of ___ because the digit moved ___ place(s) ___.” Students solve a sequence of whole-number and decimal problems, draw a place-value chart for selected items, and explain at least one answer. Teacher circulates, asks “What happened to the digit’s value?” and provides immediate feedback.

5. 25–30 min · Exit ticket and close. Display the exit-ticket and closing slide. Students independently complete: (a) (10 \times 0.8), (b) (1/10) of 60, and (c) explain one answer using a sentence frame. Teacher collects responses, asks two students to share different examples, and previews that the next lesson will extend the pattern to larger powers of 10.

Resources

• the complete place-value slide deck
• the multiply-and-divide-by-ten practice sheet
• Place-value chart for each student or pair
• Place-value disks or base-ten disks
• Whiteboards, pencils, and erasers
• Large-print, high-contrast equation cards
• Board space for sentence frames

Assessment

• During the hook and guided practice, listen for whether students distinguish a digit from its value and correctly identify the direction of movement.
• Review worksheet responses and explanations for accurate calculations, correct place-value movement, and use of the sentence frame.
• Use the exit ticket to identify students needing reteaching; mastery is at least 80% accuracy with a correct explanation.

Differentiation

• Support: Use concrete-representational-abstract modeling, place-value disks, physical left/right movements, visual arrows, repeated modeling, and one equation at a time. Reduce the number of practice items while preserving whole-number and decimal examples.
• Language and communication: Provide the sentence frames and allow students to respond verbally, by pointing, by writing, or through teacher scribing. Pair students strategically and read directions aloud.
• Dyslexia-friendly access: Use large, high-contrast print; separate symbols from words; display only one equation at a time; read equations aloud; and avoid crowded worksheets.
• Extension: Students solve missing-number equations such as (10 \times \square = 4.7) and (\square \div 10 = 0.36), then explain how multiplying or dividing by 10 affects the position and value of digits across several decimal places.