Illustrative Mathematics Grade 5, Unit 5: Place Value Patterns and Decimal Operations

What is my child learning in Unit 5?

• Noticing that each place is ten times the place to its right, so 0.03 is one tenth of 0.3. Learn more: What each digit is worth, including decimals
• Explaining why multiplying or dividing by 10 shifts every digit one place, so 2.7 × 10 = 27 and 2.7 ÷ 10 = 0.27. Learn more: Multiplying and dividing by 10, 100, and 1,000
• Writing decimals to thousandths in words, numerals, and expanded form, and comparing them, like 0.302 and 0.32. Learn more about reading and writing decimals to thousandths: Reading and writing decimals to thousandths · Learn more about comparing decimals to thousandths
• Rounding decimals to the nearest whole, tenth, or hundredth, like 0.856 to 0.86 or 0.9. Learn more: Rounding decimals, like 4.68 to 4.7
• Adding, subtracting, multiplying, and dividing decimals with place value reasoning, like 0.4 × 0.7 = 0.28 or 1.2 ÷ 0.4 = 3. Learn more about adding and subtracting decimals to hundredths: Adding and subtracting decimals to hundredths · Learn more about multiplying decimals to hundredths · Learn more about dividing decimals to hundredths

How you can help

1. 1Measure an object to the nearest millimeter with a meter stick, like 0.256 meters. Ask your child to round it to the nearest hundredth, 0.26, and nearest tenth, 0.3.
2. 2Ask what a $0.27 item costs if you buy 10 or 100 of them. Let your child explain how each digit shifts, giving $2.70 and $27.
3. 3Write 0.302 and 0.32 on a sticky note at dinner. Ask your child which is greater, 0.32, and to prove it by writing both as thousandths.

Where kids can get stuck

• Thinking 0.302 is greater than 0.32 because it has more digits.
• Mixing up the direction, so they say the 3 in 0.03 is worth more than the 3 in 0.3.
• Multiplying 0.4 × 0.7 and writing 2.8, not seeing that tenths times tenths gives hundredths.

Practice makes perfect

Bobby's Math Club has practice problems that adapt to your child’s level, each with a detailed explanation and an easy-to-follow video, so your child can build confidence in these skills one step at a time.

Words your child will hear

place value

How much a digit is worth based on its place, like ones, tens, or tenths.

thousandth

One of 1,000 equal parts of a whole, written 0.001.

expanded form

Breaking a number apart by place value, like 400 + 20 + 1.

power of 10

A number made only of 10s multiplied together, like 10, 100 (10 × 10), or 1,000 (10 × 10 × 10).

round

To change a number to a nearby, simpler one, like 4.68 to 4.7.

compare

To decide which number is greater, less, or equal, using >, <, or =.

decimal point

The dot that separates the whole number from the parts smaller than one.

hundredth

One of 100 equal parts of a whole, written 0.01 or 1/100.