Standard #: MA.5.AR.1.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.5.NSO.2.1
• MA.5.NSO.2.2
• MA.5.FR.1.1
• MA.5.GR.3.3
• MA.5.GR.4.2
• MA.5.DP .1.2

 

Terms from the K-12 Glossary

• Dividend 
• Divisor 
• Equation
• Whole Number

 

Vertical Alignment

Previous Benchmarks

• MA.3.AR.1.2 
• MA.4.AR.1.1

 

Next Benchmarks

• MA.6.NSO.2.3

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to solve multistep word problems with whole numbers and whole-number answers involving any combination of the four operations. Work in this benchmark continues instruction from grade 4 where students interpreted remainders in division situations (MA.4.AR.1.1) (MTR.7.1), and prepares for solving multi-step word problems involving fractions and decimals in grade 6 (MA.6.NSO.2.3). 

• To allow for an effective transition into algebraic concepts in grade 6 (MA.6.AR.1.1), it is important for students to have opportunities to connect mathematical statements and number sentences or equations.
• During instruction, teachers should allow students an opportunity to practice with word problems that require multiplication or division which can be solved by using drawings and equations, especially as the students are making sense of the context within the problem (MTR.5.1). 
• Teachers should have students practice with representing an unknown number in a word problem with a variable by scaffolding from the use of only an unknown box. 
• Offer word problems to students with the numbers covered up or replaced with symbols or icons and ensure to ask students to write the equation or the number sentence to show the problem type situation (MTR.6.1). 
• Interpreting number pairs on a coordinate graph can provide students opportunities to solve multi-step real-world problems with the four operations (MA.5.GR.4.2).

 

Common Misconceptions or Errors

• Students may apply a procedure that results in remainders that are expressed as r for ALL situations, even for those in which the result does not make sense. 
  • For example, when a student is asked to solve the following problem: “There are 34 students in a class bowling tournament. They plan to have 3 students in each bowling lane. How many bowling lanes will they need so that everyone can participate?” the student response is “11 r 1 bowling lanes,” without any further understanding of how many bowling lanes are needed and how the students may be divided among the last 1 or 2 lanes. To assist students with this misconception, pose the question “What does the quotient mean?”
  • It is essential to guide students in tackling real-world problems that may provide a quotient with a remainder, where interpretation may be necessary. Teachers can create environments where students relate remainders back to the contexts of the problems. For example, prompt students to consider whether it is plausible to have half of a person/object or if the problem is seeking complete groups. Remind students that interpreting remainders is contingent upon the problem's context and the specific information the problem aims to reveal. Encourage critical thinking and application of mathematical concepts in practical scenarios

 

Strategies to Support Tiered Instruction

• Instruction includes opportunities to engage in guided practice completing multi-step word problems with any combination of the four operations, including problems with remainders. Students use drawings and models to understand how to interpret the remainder in situations in which they will need to drop the remainder as their solution. 
• For example, the teacher displays and reads the following problem aloud: “There are 58 fourth grade students and 45 fifth grade students going on a class field trip. They plan to have 20 students in each van. How many vans will they need so that everyone can participate?” Students use models or drawings to represent the problem and write an equation to represent the problem. The teacher uses guided questioning to encourage students to identify that they will need to add one to the quotient as their solution. If students state that they will need 5r3 vans, the teacher refers to the models to prompt students that a sixth van is needed for the remaining three students. If students state that they will need 3 more vans since the remainder is 3, the teacher reminds students through guided questioning that the remainder of 3 represents 3 remaining students and only 1 more van is needed (i.e., “add 1 to the quotient”). This is repeated with similar multistep real-world problems, asking students to explain what the quotient means in problems involving remainders. 

• Instruction includes opportunities to engage in practice with explicit instruction completing multi-step word problems with any combination of the four operations, including problems with remainders. Students use manipulatives to understand how to interpret the remainder in situations in which they will need to drop the remainder as their solution. 
  • For example, the teacher displays and reads the following problem aloud: “There are 18 red markers and 26 black markers on the art table. Ms. Williams is cleaning up and can put 10 markers in each box. How many boxes will she need so all the markers will be put into box?” The teacher uses manipulatives (e.g., base ten blocks) to represent the problem, having students write an equation to represent the problem. The teacher uses guided questioning to encourage students to identify that they will need to add 1 to the quotient as their solution. If students state that she will need 4r4 boxes, the teacher refers to the models to prompt students that a fifth box is needed for the remaining four markers. If students state that they will need 4 more boxes since the remainder is 4, the teacher reminds students through guided questioning that the remainder of 4 represents 4 remaining markers and only 1 more box is needed (i.e., “add 1 to the quotient”). This is repeated with similar multistep real-world problems, asking students to explain what the quotient means in problems involving remainders.

 

Instructional Tasks

Instructional Task 1 (MTR.6.1) 

There are 128 girls in the Girl Scouts Troop 1653 and 154 girls in the Girl Scouts Troop 1764. Both Troops are going on a camping trip. Each bus can hold 36 girls. How many buses are needed to get all the girls to the camping site?

Instructional Task 2

Every year, Alex receives a monthly budget for buying video games. The price of video games has been increasing each year.

a. In 2020, Alex’s monthly budget for video games was $70. How many video games could he buy with one month’s budget?
b. If Alex’s budget remained $70 per month, how many video games could he buy in 2023?
c. In 2022, Alex’s monthly budget increased to $80 a month. How much did Alex’s monthly budget increase between 2020 and 2022?
d. How much more did a video game cost in 2020 than it did in 2023?
e. What would Alex’s monthly allowance need to be in 2023 in order for him to be able to buy as many video games as he could in 2020?

Instructional Task 3

Jennifer and her classmates picked 200 apples. They enjoyed snacking on 119 of the apples and then shared the remaining apples equally among nine baskets. Unfortunately, on their way to the bus, Jennifer accidentally knocked over one basket, resulting in the loss of those apples. How many apples were placed in the bus?

Instructional Task 4(MTR.7.1)

Nancy has 478 one-dollar bills that she wants to divide equally between her 7 friends.

a. How much money will each person receive? How much money will Nancy have left over?
b. Nancy exchanged the remaining one-dollar bills for nickels. If she divides the coins equally between her 7 friends, how much money will each friend get? How many nickels, if any, will remain?

 

Instructional Item 2 (MTR.3.1) 

For a fundraiser to replace the seats in the auditorium, Stanley raised $342 last month and $780 this month. He wants to buy as many seats to place in the auditorium at school as possible. Each seat costs $11. How many seats can Stanley buy?

 

Instructional Item 3

Augusta had $2,385. She spent $729 on a new computer. She wants to spend the rest of her money on different computer accessories. Each accessory cost $65. What is the maximum number of accessories Augusta can buy?

a. 25 accessories
b. 26 accessories
c. 27 accessories
d. 28 accessories