**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**5

**Strand:**Number Sense and Operations

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Equation
- Expression

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to add and subtract multi-digit numbers with decimals to the thousandths with procedural fluency. In grade 4 (MA.4.NSO.2.7), students explored the addition and subtraction of multi-digit numbers with decimals to hundredths using money and manipulatives. In grade 6, students add and subtract positive fractions with procedural fluency.- To demonstrate procedural fluency, students may choose a standard algorithm that works best for them and demonstrates their procedural fluency. A standard algorithm is a method that is efficient and accurate (MTR.3.1).
- When students use a standard algorithm, they should be able to justify why it works conceptually. Teachers can expect students to demonstrate how their algorithm works, for example, by comparing it to another method for addition and subtraction (MTR.6.1).
- Along with using a standard algorithm, students should estimate reasonable solutions before solving. Estimation helps students anticipate possible answers and evaluate whether their solutions make sense after solving.

### Common Misconceptions or Errors

- Students can make computational errors while using standard algorithms when they cannot reason why their algorithms work. In addition, they can struggle to determine where or why that computational mistake occurred because they did not estimate reasonable values for intermediate outcomes as well as for the final outcome. During instruction, teachers should expect students to justify their work while using their chosen algorithms and engage in error analysis activities to connect their understanding to the algorithm.

### Strategies to Support Tiered Instruction

- Instruction includes estimating reasonable values for sums and differences when adding and subtracting decimals to the hundredths.
- For example, students make reasonable estimates for the sum of 6.32 + 2.84. Instruction includes stating, “Before using an algorithm, we will estimate the sum to make sure that we are using the algorithm correctly and our answer is reasonable. I will use my understanding of rounding decimals to estimate my sum. The addend of 6.32 rounds to 6 when rounded to the nearest whole number and reasonable estimate for my sum would be 9 because 6 + 3 = 9.”
- For example, students make reasonable estimates for the difference of 7.9 − 4.25. Instruction includes stating, “Before using an algorithm, we will estimate the difference to make sure that we are using the algorithm correctly and our answer is reasonable. I will use my understanding of rounding decimals to estimate my difference. The minuend of 7.9 rounds to 8 when rounded to the nearest whole number and the subtrahend 4.25 rounds to 4 when rounded to the nearest whole number. A reasonable estimate for my difference would be 4 because 8 − 4 = 4.” the addend 2.84 rounds to 3 when rounded to the nearest whole number.

- Instruction includes explaining and justifying mathematical reasoning while using an algorithm to add and subtract decimals to the hundredths. Instruction also includes determining if an algorithm was used correctly by analyzing any errors made and reviewing the reasonableness of solutions.
- For example, students use a standard algorithm to determine 6.32 + 2.84 and explain their thinking using a place value understanding. Instruction includes stating, “Begin by lining up the decimal points and place values for each addend. Next, add in hundredths place. 2
*hundredths plus*4*hundredths**are*6*hundredths*. Because the total number of*hundredths*is less than 10*hundredths*it is not necessary to regroup. Next, add in the tenths place. 3*tenths**plus*8*tenths**are*11*tenths*. Because I have more than 10*tenths*it is necessary to regroup the 10*tenths*to make one whole. After composing a group of 10 tenths there is 1 tenth remaining. Finally, add 6*ones*plus 2*ones*and the 1 whole that was regrouped from the tenths place. The sum is 9.16. Our sum of 9.16 is close to our estimate of 9, this helps us determine that our answer is reasonable.”

- For example, students use a standard algorithm to determine 7.9 − 4.25 and explain their thinking using place value understanding. The teacher reminds students that 7.9 is equivalent to 7.90 and uses a decimal grid to show the equivalency of 0.9 and 0.90 if needed. Instruction includes stating, “Begin by lining up the decimal points and place values. Next, subtract 4.25 starting in the
*hundredths*place. There are not enough*hundredths*to subtract 5*hundredths*from 0*hundredths*. It is necessary to decompose one tenth into 10*hundredths*. Now there are 10*hundredths*, and there is enough to subtract 5*hundredths*. 10*hundredths*− 5*hundredths*= 5*hundredths*. Then, subtract the*tenths*: 8*tenths*− 2*tenths*= 6*tenths*. Finally, subtract the*ones*: 7*ones*− 4*ones*= 3*ones*. The difference is 3.65. Our difference of 3.65 is close to our estimate of 4, this helps us determine that our answer is reasonable.”

- For example, students use a standard algorithm to determine 1.9 + 2.3 and explain their thinking using a place value understanding. Instruction includes stating, “Begin by lining up the decimal points and place values for each addend. Next, add in
*tenths*place. 9*tenths plus*3*tenths**are*12*tenths*. Because I have more than 10*tenths*it is necessary to regroup the 10*tenths*to make one whole. After composing a group of 10*tenths*there are 2*tenths*remaining. Finally, add 1*one*plus 2*ones*and the 1 whole that was regrouped from the*tenths*place. The sum is 4.2. Our sum of 4.2 is close to our estimate of 4, this helps us determine that our answer is reasonable.”

- For example, students use a standard algorithm to determine 5.2 − 3.8 and explain their thinking using place value disks and their understanding of place value. Instruction includes stating, “Begin by lining up the decimal points and place values. Next, subtract 3.8 starting in the
*tenths*place. There are not enough*tenths*to subtract 8*tenths*from 2*tenths*. It is necessary to decompose one whole into 10*tenths*. Now there are a total of 12*tenths*, and there are enough to subtract 8*tenths*. 12*tenths*– 8*tenths*= 4*tenths*. Finally, subtract the*ones*: 4*ones*– 3*ones*= 1*one*. The difference is 1.4. Our difference of 1.4 is close to our estimate of 1, this helps us determine that our answer is reasonable.”

- Instruction includes the use of place value columns to support place value understanding when using an algorithm to add and subtract decimals.

### Instructional Tasks

*Instructional Task 1* (MTR.3.1)

*eight hundred two and forty*-

*Six thousandths*and

*three hundred and nine tenths*. Explain how you use your algorithm to subtract.

### Instructional Items

*Instructional Item 1*

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Educational Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Experts

## Tutorial

## STEM Lessons - Model Eliciting Activity

On this MEA activity, students will create a procedure to rank five lunch bags as to which one is the best in keeping food and drinks at a safe temperature and appealing to the taste, while keeping design and price on target.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Students work in teams to plan the contents of a covered wagon for a family relocating from Missouri to Oregon. Students must calculate the weight and cost of the wagon by adding, subtracting, and multiplying with decimals.

## MFAS Formative Assessments

Students are asked to solve a word problem that involves adding two decimals by using a strategy based on place value.

Students are asked to solve a word problem that involves subtracting two decimals by using a strategy based on place value.

## Original Student Tutorials Mathematics - Grades 6-8

Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial.

Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.

## Student Resources

## Original Student Tutorials

Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.

Type: Original Student Tutorial

Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial.

Type: Original Student Tutorial

## Educational Games

This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

*Addition/**Subtraction:* The addition and subtraction of whole numbers, the addition and subtraction of decimals.

*Multiplication/Division: *The multiplication and addition of whole numbers.

*Percentages: *Identify the percentage of a whole number.

*Fractions: *Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

This interactive applet gives students practice in making change in U.S. dollars and in four other currencies. Students are presented with a purchase amount and the amount paid, and they must enter the quantity of each denomination that make up the correct change. Students are rewarded for correct answers and are shown the correct change if they err. There are four levels of difficulty, ranging from amounts less than a dollar to amounts over $100.

Type: Educational Game

## Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

## Parent Resources

## Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial