Using proportional reasoning (Gr 7 & 8)

content

Curriculum

Grade 7:

B2.2 understand and recall commonly used percents, fractions, and decimal equivalents

B2.3 use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used

B2.10 identify proportional and non-proportional situations and apply proportional reasoning to solve problems

Grade 8:

B1.4 use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems

B2.3 use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used

B2.5 add and subtract fractions, using appropriate strategies, in various contexts

B2.6 multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts

B2.8 compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts

C1.1 identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values

Knowledgehook's Math Background, Misconception Charts and Gap Closing Resources

These resources are available in your Knowledgehook account. They are also linked in this Google Doc. However, you must be logged into your browser or app with your DSB1 account to access this file.

Knowledgehook's math background charts explore the big ideas in detail and address best practices and tips for remediation. Their misconceptions charts include tips for understanding, preventing, and/or remediating common learning gaps, misconceptions, and errors for this topic. The Remediation questions can be assigned to students in order to assess individual students' specific remediation needs.

Topics for this unit:

Adding, Subtracting, Multiplying and Dividing Fractions
Describing and Representing a Percent
Describing and Representing Ratios
Equivalent Forms of Ratios
Equivalent Forms of Rates
Greatest Common Factor and Least Common Multiple
Representing and Comparing Rational Numbers
Solving Rate Problems
Solving Percent Problems
Solving Proportion Problems

Grade 7 & 8 Knowledgehook Support Charts

Marian Small's Gap Closing

Gap Closing resources are designed for students who need additional support in mathematics. For each topic in the resource, there is a diagnostic and a set of intervention materials. Diagnostics are designed to uncover the typical problems students have with a specific topic.

Proportional Reasoning

Decimals

Fractions

Pedagogy

Sample Lesson

Lesson Overview

Seeing Proportional Relationships Lesson

Lesson Planning Notes

teacher.desmos.com/activitybuilder/custom/5fda35e150e5670d2eaca0c1

Desmos Lesson

Proportional Relationships • Teacher Guide.pdf

PDF Lesson Guide

Pedagogical Teacher Support Documents

BigIdeasQuestioning_ProportionalReasoning.pdf

Big Ideas & Questions for Proportional Reasoning

proportionreason.pdf

Paying Attention to Proportional Reasoning

Mental Math Resources

Estimation180.com is a great site with tons of estimation challenges that build number sense and problem-solving skills. They contain many activities that encourage mental math strategies like the ones outlined in expectation B2.3 in this unit. You could also use them for Number Talk topics or daily bell work. These are open tasks that are helpful for building number sense in academically diverse classrooms.

Read a short blog post outlining one teacher's facilitation strategies and the learning outcomes of using Estimation180 challenges.
Listen to the Estimation180 podcast (accessible on any device).
Follow on Twitter: @Estimation180 and @mr_stadel
Check out Estimation180's Teacher Guide and Math Reasoning Framework with Daily Log.
You could also make your own daily Google Form or Desmos Activity to record student answers and thinking.
- - How to Create Your Own Estimation180 Google Form
  - Estimation180 Desmos Activity Template (Click "Copy and Edit" from the activity options.)

Visual Lesson Approaches to Support Student Understanding

Desmos

access create your free teacher account at teacher.desmos.com
Desmos support page
Many of these activities are also available in French

Desmos activities for this topic:

Online simulations that power inquiry and understanding

Gizmos

Gizmos for this topic include:

MathIsVisual.com

"This website was created to assist in building a better conceptual understanding of mathematics through the use of visuals. The images, videos and resources shared here are intended to help all teachers, parents and students understand that Math Is Visual and we should take every opportunity to teach it that way."

Kyle Pearce's blog post on maximizing the effectiveness of these resources
1,3 How To Convert Units of Measurement Visually

Mathematical Modelling Tasks

3-Act math tasks are a great way to weave together proportional reasoning and mathematical modelling. Visit the Mathematical Modelling page on this site for lots of 3-act math task resources.

3-Act Tasks Involving Proportional Reasoning:

Hot Chocolate

Jugs of Milk

Assessment Ideas

Assessment: Open Questions for Proportional Reasoning

Open Questions Organized by Big Idea

Assessment: Parallel Questions for Proportional Reasoning

Parallel Tasks for Proportional Reasoning

Introductory Video

Knowledgehook

Knowledgehook is an Instructional Guidance System (IGS) that uses engaging assessments to unlock insights and expert guidance for math teachers.

Knowledgehook Support Page

Triangulating Assessment Data

Use ongoing, progressive rubrics to record student progress based on triangulated data, like observations and conversations.

(Sample template for Reasoning & Proving Rubric)
(Sample template for Number: B2)

Here's a great blog post by Damian Cooper called What is “Triangulation” in the Assessment Context?, which will help support our understanding of how we can assess as we move towards giving students messier and more real problems where the process of problem-solving is valued in addition to "the right answer."

B2: Documenting Conversation & Observations - Data.pdf

You can use Google Forms to quickly document evidence of learning during your conversations with and observations of your students. This PDF includes links to several Google Forms organized by strand. You'll need to copy and modify them to include your students' names.

Google Forms for Documenting Student Learning.pdf

Use Showbie to create Problem-Solving Portfolios where students can work on problems with increasing complexity as they master the concepts and monitor their progress.

technology

Digital Manipulatives

Colour tiles

Number Line

Fraction Strips

Relational Rods+

Geoboard