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  • = Denotes Benchmark Expectation

  • = Includes a Feedback Box

Benchmark Expectations. Several of the Expectations are prioritized as Benchmark Expectations because they are particularly important concepts and skills to be learned in this unit. Benchmark Expectations identify the concepts and skills that are central to the unit, are prerequisites for learning content in an upcoming unit, are the last significant opportunity for assessment in the curriculum or grade, or are concepts commonly associated with difficulties or misconceptions. These Expectations are marked with a red circle in the Key Assessment Opportunities Chart.

Feedback Boxes. Feedback Boxes Feedback Boxes are provided with several activities to report progress toward these Expectations. Look for the box ( ) on the Unit 8 Key Assessment Opportunities Chart.. See Figure 2. In this unit, students will also get better acquainted with the Math Practices Expectations by discussing them in the context of a specific problem, receiving feedback, reviewing a peer's work, and revising their own work.

Add and Subtract Decimals Quiz
Feedback Box		 Expectation Check
In		 Comments
Represent numbers to the thousandths using symbols, area models, base-ten pieces, and number lines. [Q# 1C, 2C] E1
Compare decimals to the thousandths using place value understanding. [Q# 1C, 2D] E3
Add and subtract decimals to the thousandths using models and strategies. [Q# 1A–B, 2A–B] E7
Estimate decimal differences. [Q# 3] E9
Yes … Yes, but … No, but … No, …
MPE2. Find a strategy. I choose good tools and an efficient strategy for solving the problem. [Q# 1A–B, 2A–B]

Figure 2: Sample Feedback Box from Lesson 8

Key Assessment Opportunities Chart Print

L1SG Measuring Stacks Check-In: Q# 11–12
Key Ideas in Unit 8

L1 SG

L1 DPP

L2 SG

L3 SAB

L3 SG

L4 TG

L5 SG

L6 SG

L7 TG

L7 DPP

L8 TG

L9 SG

L9 DPP

L10 SG

L10 SG

L11 SG

L11 TG

L11 DPP
Unit 8 Expectations

Math Content

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Content Expectations. The Expectations assessed in this unit focus on concepts of decimals and fractions. Because all the Algebra Key Ideas arise from and are closely connected to ideas in the other content strands, Expectations related to algebra will also be listed under a second content strand. For example:

Number 1. Number Sense: Understand the base-ten number system, recognize relationships among quantities and numbers, and represent numbers in multiple ways.

E6. Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of ten. (Algebra 4)

The Content section of the Unit 8 Key Assessment Opportunities Chart identifies some of the activities in the unit that are appropriate for assessing students' abilities with Expectations related to these number concepts. The Math Facts section of the same chart identifies activities in the unit that are appropriate for assessing students' multiplication and division facts strategies.

Number 1

Number Sense: Understand the base-ten number system, recognize relationships among quantities and numbers, and represent numbers in multiple ways.

E1

 Represent numbers to the thousandths using fractions, decimals, words, area models, baseten pieces, number lines, and expanded form. [5.NBT.3] [MP2, 4, 5, 7]

E2

 Make connections among representations of decimals including fractions, words, area models, base-ten pieces, number lines, and number sentences. [5.NBT.3] [MP2, 4, 5, 7]

E3

 Compare and order decimals to the thousandths using place value understanding and benchmarks. (Algebra 3) [5.NBT.3] [MP2, 3, 4, 5, 6]

E4

 Round decimals using place value understanding. [5.NBT.4] [MP1, 2, 3, 4, 5, 6, 7]

E5

 Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. [5.NBT.1] [MP2, 4, 6, 7, 8]

E6

 Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of ten. (Algebra 4) [5.NBT.2] [MP2, 4, 6, 7, 8]

Number 2

Operations: Understand the meaning of numerical operations and their application for solving problems.

E7

 Add and subtract decimals to the thousandths using models and strategies. [5.NBT.7] [MP1, 2, 3, 4, 5, 6, 7, 8]

E8

 Multiply and divide decimals using models and strategies. [5.NBT.7] [MP1, 2, 3, 4, 5, 6, 7, 8]

Number 3

Computation and Estimation: Use efficient and flexible procedures to compute accurately and make reasonable estimates.

E9

 Estimate sums, differences, products, and quotients involving decimals and fractions. [5.NBT.7] [MP1, 2, 3, 4, 5, 6, 7, 8]

Data 2

Data Representation: Select and create appropriate representations, including tables and graphs, for organizing, displaying, and analyzing data.

E10

 Use data tables and graphs to organize and display data involving decimal values. (Algebra 2) [5.G.2] [MP4, 5, 6]

Data 3

Data Description. Describe a data set by interpreting graphs, identifying patterns, and using statistical measures, e.g., average and range.

E11

 Describe a data set by interpreting graphs and data tables, identifying patterns, and using the median. [5.G.2, 6.SP.5] [MP2, 3, 4, 5, 6]

Data 4

Using Data. Apply relationships and patterns in data to solve problems, develop generalizations, and make predictions.

E12

 Use relationships and patterns in a data set to make claims and predictions. (Algebra 4) [5.OA.3] [MP1, 4, 5, 6, 7, 8]

Number 3

Computation and Estimation: Use efficient and flexible procedures to compute accurately and make reasonable estimates.

E13

 Demonstrate fluency with the multiplication and division facts. [5.NBT.5, 6]

Math Practices

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Math Practices Expectations. Students use the Math Practices Expectations on the Math Practices page in the Math Practices page in the Student Guide Reference section to help them focus on practices related to both problem solving and communication. Students become more comfortable with these Expectations by reviewing them before, during, and after solving a problem and by deciding how well they are met in their work and the work of others.

 

The Math Practices section of the Unit 8 Key Assessment Opportunities Chart identifies activities in the unit that are appropriate for assessing students' use and development of the math practices related to problem-solving habits and communication skills. In this unit, students will focus on knowing the problem [MPE1], finding a strategy [MPE2], and showing their work [MPE5].
MPE1 Know the problem. I read the problem carefully. I know the questions to answer and what information is important. [MP1]
MPE2 Find a strategy. I choose good tools and an efficient strategy for solving the problem. [MP1, 2]
MPE3 Check for reasonableness. I look back at my solution to see if my answer makes sense. If it does not, I try again. [MP6]
MPE4 Check my calculations. If I make mistakes, I correct them.
MPE5 Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking. [MP2, 4, 5]
MPE6 Use labels. I use labels to show what numbers mean. [MP6]