# Teaching 4.NF.C.7 – Compare Two Decimals to Hundredths by Reasoning about their Size

## Number & Operations – Fractions – 4th Grade

#### Understand decimal notation for fractions, and compare decimal fractions.

CCSS.Math.Content.4.NF.C.7
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Teacher Notes
Decimal comparisons, like fraction comparisons, are only valid if the whole is the same size. There are multiple ways to compare decimals (place value positions, visual models, estimation) just as there are multiple ways to compare whole numbers.
Students may think that a decimal is the decimal point rather than a number. Students need to understand that the decimal point is a symbol that indicates the location of the ones place and all other subsequent place values in the decimal system. The decimal point separates the whole number amount from a number that is less than one.

Student Knowledge Goals

I know how to read and write decimals through the hundredths.
I know comparisons are valid when the two decimals refer to the same whole.
I can compare two decimals by reasoning about their size.
I can justify conclusions about the comparison of decimals using visual models and other methods.
I can relate a decimal to a whole number.
I can use what I know about fractions to help me compare decimals.

Vocabulary
comparison symbols (<, >, =)
decimals
hundredths
tenths
visual models for decimals (grid paper, number line, base ten blocks etc.)
whole

Lessons
Engage NY Module 6 C-9 – Use the place value chart and metric measurement to compare decimals and answer comparison questions.
Engage NY Module 6 C-10 – Use area models and the number line to compare decimal numbers, and record comparisons using <, >, and =.
Engage NY Module 6 C-11 – Compare and order mixed numbers in various forms.
Engage NY Module 6 D-12 – Apply understanding of fraction equivalence to add tenths and hundredths.
Engage NY Module 6 D-13 – Add decimal numbers by converting to fraction form.

Student Video Lessons
Learn Zillion – Compare two decimals to hundredths by reasoning about their size
Virtual Nerd – Comparing decimals
Study Jams – Comparing decimals on a number line

Online Problems and Assessments
Khan Academy – Questions and Video Lessons
Compare money amounts
Compare decimals on number lines
Compare decimal numbers
Put decimal numbers in order
Put tricky decimals in order
Compare fractions and decimals on number lines

Online Games
Comparing Decimals