## 5th Grade Formative Assessment Lessons

## Division and Interpreting Remainders

This concept-based lesson is intended to help you assess how well students are able to use a variety of strategies to multiply. In particular, this unit aims to identify and help students who have difficulties with the traditional division algorithm,representing division in multiple ways, and interpreting remainders.

This lesson involves a range of

This lesson asks students to select and apply mathematical content from across the grades, including the CCSS

This lesson involves a range of

*mathematical practices*from the standards, with emphasis on:**Reason abstractly and quantitatively, Look for and make use of structure, Look for and make use of repeated reasoning.**This lesson asks students to select and apply mathematical content from across the grades, including the CCSS

**Number and Operations in Base Ten:****5-NBT: Perform operations with multi-digit whole numbers and****6-NS: Compute fluently with multi-digit numbers and find common factors and multiples.**## Pizza with Friends

This lesson unit is intended to help you assess how well students are able to model addition and subtraction of fractions. In particular, this unit aims to identify and help students who have difficulties with: Using equivalent fractions to add and subtract fractions, Using benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers, and Solving word problems involving the addition and subtraction of fractions.

This lesson asks students to select and apply mathematical content from across the grades, including the CCSS

This lesson involves a range of S

This lesson asks students to select and apply mathematical content from across the grades, including the CCSS

**Number and Operations 5.NF****Use equivalent fractions as a strategy to add and subtract fractions.**This lesson involves a range of S

*tandards for Mathematical Practice,*with emphasis on:**1. Make sense of problems and persevere in solving them, 3. Construct viable arguments and critique the reasoning of**

others, 4. Model with mathematics, 7. Look for and make use of structure.others, 4. Model with mathematics, 7. Look for and make use of structure.

## Volume

This lesson is intended to help you assess how well students are able to model three dimensional figures and find their volume. In particular, this unit aims to identify and help students who have difficulties with: Recognizing volume as an attribute of three-dimensional space. Measuring volume by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. Measuring necessary attributes of shapes, in particular the base area, in order to determine volumes to solve real world and mathematical problems.

**This lesson involves***mathematical content*in the standards from across the grade, with emphasis on: Measurement and Data 5.MD**Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.****This lesson involves a range of***Standards for Mathematical Practice*with emphasis on:**Make sense of problems and persevere in solving them. Model with mathematics. Look for and make use of structure.**## 5th Grade Multiplying and Dividing Decimals (NOV 2012)

This lesson is intended to help you assess how well students understand the result of multiplying and dividing by a decimal less than and greater than one and what strategies they use to perform these operations. It will help you to identify students who have the following difficulties:

Lack of conceptual understanding of the properties of numbers

Do not see the relationship between multiplication and division

Applying efficient strategies to multiply and divide with decimals to hundredths.

Lack of conceptual understanding of the properties of numbers

Do not see the relationship between multiplication and division

Applying efficient strategies to multiply and divide with decimals to hundredths.

**This lesson involves***mathematical content*in the standards from across the grade, with emphasis on:**Number and Operations in Base Ten 5.NBT.7****Perform operations with multi-digit whole numbers and with decimals to hundredths.****This lesson involves a range of Standards for Mathematical Practice, with emphasis on:****Reason abstractly and quantitatively.**__Formative Assessment Lessons written by other organizations__

## Stuffed with Pizza written by New York City Department of Education

In this unit, students will develop and expand the concept of rational numbers by using several interpretations and different types of physical models. Students will explore their own ways of inventing algorithms to perform operations with rational numbers and they will also understand the mathematics behind the traditional algorithms to do operations with rational numbers. The Formative Assessment Lesson is embedded in the unit.

Common Core Standards addressed:

This lesson involves a range of S

Common Core Standards addressed:

**5.NF Use equivalent fractions as a strategy to add and subtract fractions.**This lesson involves a range of S

*tandards for Mathematical Practice,*with emphasis on:**1. Make sense of problems and persevere in solving them, 3. Construct viable arguments and critique the reasoning of**

others, 6. Attend to Precision.others, 6. Attend to Precision.