Mathematics · Grade 5 · The Power of Place: Large Numbers and Decimals · Term 1

Multiplying by Powers of Ten

Students will explore the patterns that emerge when multiplying whole numbers and decimals by powers of ten.

• Ontario Curriculum Expectations
• 5.NBT.A.2

About This Topic

Multiplying whole numbers and decimals by powers of ten reveals clear patterns in place value. For whole numbers, such as 45 multiplied by 100 equals 4500, students see zeros added to the right. With decimals, 4.5 times 100 shifts the decimal point two places right to 450. Students predict results, like a decimal times 100, explain the decimal movement connection, and trace how digit values multiply by the power of ten. These align with Ontario Grade 5 standards for explaining patterns.

In the unit on large numbers and decimals, this topic builds strong number sense and prepares for scientific notation and multi-digit operations. Students analyze shifts across examples, fostering recognition of the structure of the base-ten system.

Active learning benefits this topic greatly with visual and kinesthetic tools. Base-10 blocks let students physically shift units, rods, and flats to show multiplication effects. Collaborative chart-building uncovers patterns collectively, turning abstract rules into observable truths students own.

Key Questions

1. Predict the outcome when a decimal is multiplied by 100.
2. Explain the relationship between moving the decimal point and multiplying by powers of ten.
3. Analyze how the value of a digit changes when it shifts places due to multiplication by a power of ten.

Learning Objectives

• Calculate the product of a whole number or decimal and a power of ten (e.g., 10, 100, 1000).
• Explain the pattern of decimal point movement when multiplying by powers of ten.
• Analyze how the value of a digit changes when multiplied by powers of ten.
• Predict the result of multiplying a given decimal by a specified power of ten.

Before You Start

Understanding Place Value for Whole Numbers

Why: Students need a solid grasp of place value to understand how digits shift and change value when multiplied.

Understanding Place Value for Decimals

Why: This topic extends place value concepts to decimals, requiring students to understand tenths, hundredths, and thousandths.

Basic Multiplication Facts

Why: Students must be able to perform basic multiplication to understand the patterns when multiplying by powers of ten.

Key Vocabulary

Power of Ten	A number that can be expressed as 10 raised to an integer exponent (e.g., 10, 100, 1000).
Place Value	The value of a digit based on its position within a number, such as ones, tens, hundreds, or tenths, hundredths.
Decimal Point	A symbol used to separate the whole number part of a number from its fractional part.
Digit Value	The specific value a digit represents based on its place value in a number.

Watch Out for These Misconceptions

Common Misconception

Multiplying a decimal by 10 makes the number smaller.

What to Teach Instead

Multiplication by powers of ten always increases value by shifting the decimal right. Number line activities let students plot originals and products, visually confirming growth. Pair discussions help revise initial ideas through evidence.

Common Misconception

The decimal point moves left when multiplying by powers of ten.

What to Teach Instead

The point moves right the number of places equal to the power. Place value mats with sliders correct this kinesthetically as students manipulate digits. Group challenges reinforce the rule through repeated practice.

Common Misconception

You add the same number of zeros regardless of whole or decimal numbers.

What to Teach Instead

For decimals, zeros fill after the shifted point. Base-10 block regrouping shows exact changes without arbitrary adds. Collaborative sorts of examples clarify distinctions quickly.

Active Learning Ideas

Manipulative Shift: Base-10 Blocks

Give students base-10 blocks to represent decimals like 0.45. Instruct them to multiply by 10 or 100 by regrouping blocks and shifting positions. Pairs record before-and-after sketches and share patterns with the class.

30 min·Pairs

Pattern Hunt: Number Grids

Small groups create grids with numbers from 1.23 to 12.3, multiplying each by 10, 100, and 1,000. They highlight digit shifts and decimal movements. Groups present one key pattern to the class.

35 min·Small Groups

Relay Race: Decimal Multipliers

Prepare cards with decimals and powers of ten. Pairs line up; one solves a card, tags partner to run next. First pair finishing all correctly wins. Review answers whole class.

20 min·Pairs

Scale Models: Classroom Measures

Small groups measure objects like desks in cm, multiply by 10 or 100 for meters or larger scales. Plot scaled versions on graph paper. Discuss real-world applications.

40 min·Small Groups

Real-World Connections

• Scientists often multiply measurements by powers of ten to express very large or very small quantities, such as the distance to stars in kilometers or the size of microscopic organisms in meters.
• Financial analysts use multiplication by powers of ten when working with large sums of money, like national budgets or company revenues, to simplify calculations and reporting.
• When using a microscope, the magnification factor (often a power of ten) is multiplied by the initial measurement to determine the actual size of the specimen being viewed.

Assessment Ideas

Quick Check

Present students with a series of problems like '3.14 x 10 = ?' and '56 x 100 = ?'. Ask them to write the answer and then briefly explain the rule they used to get it.

Exit Ticket

Give students a decimal, for example, 0.75. Ask them to calculate the product of this decimal multiplied by 10, 100, and 1000. On the back, they should explain how the decimal point moved for each calculation.

Discussion Prompt

Pose the question: 'How does multiplying 25 by 100 change the value of the digit '2'?' Guide students to explain that the '2' in 25 represents 2 tens (20), but in 2500, it represents 2 thousands (2000), a change of 100 times its original value.

Frequently Asked Questions

How do you teach multiplying decimals by powers of ten in grade 5 Ontario math?

Start with patterns using visual models like place value charts. Students multiply familiar numbers by 10, then 100, noting decimal shifts. Connect to key questions by having them predict and explain changes. Reinforce with real contexts like scaling recipes, ensuring alignment with 5.NBT.A.2 expectations.

What are common student errors with powers of ten multiplication?

Errors include shifting decimals left or assuming all multiplications just add zeros. Address by contrasting whole number and decimal examples side-by-side. Visual tools reveal patterns, while error analysis discussions build self-correction skills over time.

How can active learning help students master multiplying by powers of ten?

Active approaches like base-10 manipulatives make shifts tangible; students physically move blocks to see values grow. Games and relays add engagement, practicing fluency without rote drill. Group pattern hunts promote talk, where peers challenge misconceptions and solidify rules collaboratively.

Why focus on patterns in powers of ten for grade 5 place value?

Patterns link multiplication to place value shifts, deepening number sense for larger operations. In Ontario curriculum, it supports unit goals on decimals and big numbers, setting up scientific notation. Students who grasp this predict outcomes confidently and analyze digit impacts accurately.