MA.6.AR.3.3

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Extend previous understanding of fractions and numerical patterns to generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.

Examples

The table below expresses the relationship between the number of ounces of yellow and blue paints used to create a new color. Determine the ratios and complete the table.

 

Yellow (part) 1.5 3 9
 Blue (part)24  
 New Color (whole)  12 21

 

Clarifications

Clarification 1: Instruction includes using two-column tables (e.g., a relationship between two variables) and three-column tables (e.g., part-to-part-to-whole relationship) to generate conversion charts and mixture charts.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Algebraic Reasoning
Standard: Understand ratio and unit rate concepts and use them to solve problems.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Rate
  • Unit Rate

 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In elementary grades, students developed understanding of fraction concepts and operations, often in the context of the relationship that relates parts to wholes. In grade 6, students use tables to display parts to parts and parts to whole relationship, as preparation for understanding a constant ratio relationship between two quantities. In grade 7, students will achieve a more formal understanding of the constant of proportionality and proportional relationships, which can be represented by tables, equations and graphs. 
  • Instruction includes discussion about how the patterns that students see in the tables can help them reason through various situations (MTR.4.1, MTR.5.1).
  • Instruction includes the use of acting out scenarios, bar models, tables and number lines in order to see relationships and relevance to real-world application (MTR.2.1).
    • Bar Model
      3 yellow colored boxes and 4 blue colored boxes
    • Tables
      tables with row names Yellow, Blue, New color
    • Number Lines
      Number line

Common Misconceptions or Errors

  • Students may be looking for arithmetic or counting patterns within the table and not seeing multiplicative patterns between the ratio values.

 

Strategies to Support Tiered Instruction

  • Instruction includes the use of whole number parts to allow for students to explore the various relationships in the tables before introducing positive rational values. Discussions include additive and multiplicative patterns amongst the rows and the columns of the table.
  • Instruction includes the use of two different counters to represent the provided ratios with emphasis on the different colors representing the parts and the total number of counters representing the whole. Teacher allows for opportunities for the student to explore equivalent ratios by adding addition sets of counters or by dividing the existing counters into equal groups and recording the equivalent ratios in a two-or three-column table.
    • For example, students can use the counters to help complete the table to express the relationship between the number of students and the number of adults on a recent field trip.
      3 red color circles and 1 yellow color circle
      Table containing the data of Students, Adults, and Total People

 

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.7.1)
Jeremy is making punch for a party. The relationship between the cups of syrup and the cups of water he used to create the punch mixture is shown on the table below. 
  • Part A. Complete the table. Explain the process you used to complete the table.
    Table containing the values 1 1/3, 7, 3, 12, 15, 18 3/4, and 20.
  • Part B. If Jeremy needs 30 cups of punch, how many cups of syrup are needed? How many cups of water are needed?

Instructional Task 2 (MTR.3.1)

Given the table below, determine the common ratio between the x-and y-values.

Table with columns x and y with values 2, 8, 5, 20.

 

Instructional Items

Instructional Item 1
Shambria is making pies and part of the recipe she uses is described in the table below.
Table with columns Number of Pies, Cups of Sugar, and Pounds of Apples
Using this recipe, complete what is the amount of sugar and apples needed to bake 5 pies?

Instructional Item 2 
The table below describes the same rate at which Drew hiked along the Appalachian Trail each day. Complete the table and determine how many miles he could hike in 2 hours.

Table with Rows time and distance.

 

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

Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.AR.3.AP.3: Given a visual representation, write or select a ratio that describes the ratio relationship between part-to-part and part-to-whole ratios.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessment

Making Coffee:

Students are asked to write ratios equivalent to a given ratio.

Type: Formative Assessment

Original Student Tutorial

Helping Chef Ratio:

You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Mixing Concrete:

Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

Type: Problem-Solving Task

MFAS Formative Assessments

Making Coffee:

Students are asked to write ratios equivalent to a given ratio.

Original Student Tutorials Mathematics - Grades 6-8

Helping Chef Ratio:

You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Helping Chef Ratio:

You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Mixing Concrete:

Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Task

Mixing Concrete:

Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

Type: Problem-Solving Task