Students expand their conception of what a “number” is as they are introduced to an entirely new category of number, decimals, which they learn to convert, compare, and add in simple cases.
Math
Unit 6
4th Grade
Unit 6 introduces students to an entirely new category of number—decimals. Students will explore decimals and their relationship to fractions, seeing that tenths and hundredths are particularly important fractional units because they represent an extension of the place value system into a new kind of number called decimals. Thus, students expand their conception of what a “number” is to encompass this entirely new category, which they will rely on for the remainder of their mathematical education.
Students have previously encountered an example of needing to change their understanding of what a number is in Grade 3, when the term came to include fractions. Their Grade 3 understanding of fractions (3.NF.A), as well as their work with fractions so far this year (4.NF.A, 4.NF.B), will provide the foundation upon which decimal numbers, their equivalence to fractions, their comparison, and their addition will be built. Students also developed an understanding of money in Grade 2, working with quantities either less than one dollar or whole dollar amounts (2.MD.8). But with the knowledge acquired in this unit, students will be able to work with money represented as decimals, as it so often is.
Thus, students rely on their work with fractions to see the importance of a tenth as a fractional unit as an extension of the place value system in Topic A, then expand that understanding to hundredths in Topic B. Throughout Topics A and B, students convert between fraction, decimal, unit, and expanded forms to encourage these connections (4.NF.6). Then students learn to compare decimals in Topic C (4.NF.7) and add decimal fractions in Topic D (4.NF.5). Finally, students apply this decimal understanding to solve word problems, including those particularly related to money, at the end of the unit. Thus, the work with money (4.MD.2) supports the major work and main focus of the unit on decimals.
While students will have ample opportunities to engage with the standards for mathematical practice, they’ll rely heavily on looking for and making use of structure (MP.7), particularly the structure of the place value system. They will also construct viable arguments and critique the reasoning of others (MP.3) using various decimal fraction models to support their reasoning.
In Grade 5, students will build on this solid foundation of decimal fractions to develop an even deeper understanding of decimals' relationship to place value and to perform decimal operations with similar models (5.NBT.1—4, 5.NBT.7). By the end of 6th grade, students will be fluent with the use of the standard algorithm to compute with decimals (6.NS.3). From that point forward, students will use their understanding of decimals as a specific kind of number in their mathematical work, including ratios, functions, and many others.
Pacing: 16 instructional days (14 lessons, 1 flex day, 1 assessment day)
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The following assessments accompany Unit 6.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 9.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Area model |
Example: The following shape represents 1 whole. 0.24 of it is shaded. |
Number line |
Example: The point on the number line below is located at 0.24. |
Pictorial base ten blocks |
Example: Represent 21.53 with base ten blocks. |
decimal expanded form
decimal number
decimal point
decimal fraction
fraction expanded form
hundredth
tenth
To see all the vocabulary for Unit 6, view our 4th Grade Vocabulary Glossary.
Word Problems and Fluency Activities
Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills.
Topic A: Understanding Tenths
Topic B: Understanding Tenths and Hundredths
Topic C: Decimal Comparison
Topic D: Decimal Addition
Topic E: Money as a Decimal Amount
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 5
Fraction Operations
Unit 7
Unit Conversions