Ratio Tables: Teacher Notes

Overview

In this activity, students solve proportion problems using ratio tables and compare this strategy with other strategies.

Important Mathematical Ideas

  • A proportion is an equation showing equivalent ratios.
  • A ratio table is an organized display of equivalent ratios.
  • A ratio table can be used to solve proportions and proportion problems.

Prior Knowledge

  • Determining equivalent ratios using a multiplier (whole number and fractional).
  • Expressing equivalent ratios in lowest terms.

Common Misconceptions

  • Using addition rather than multiplication to compare numbers, (e.g., the ratio 4 : 6 is equivalent to the ratio 6 : 8 since you added 2 to each of the terms) .
  • An inability to determine an equivalent ratio when the terms are not whole numbers or when the terms of one ratio are not integer multiples of the terms of the other.

Curriculum Notes

  • This activity involves one method of solving proportions - ratio tables. Expectation (NA1.03) is partially covered since it requires solving “using a variety of methods”.
  • Using ratio tables encourages proportional thinking.

Information to Support/ Enhance/ Extend Learning

  • Students are asked to keep a journal for each unit in the course. It should contain notes of important mathematical ideas with examples and new vocabulary.
  • ePortfolio may be used for these journal entries.
  • Students can make individual choices whether this is a paper or digital personal resource.
  • Consider a variety of formats as alternatives to journal entries (e.g., student note, pair/share, group discussion, exit card, poster, electronic posting).
  • Develop a Word Wall and continue it throughout the unit as new vocabulary and terms arise that require clarification (e.g., ratio tables, proportions).

Minds On

Task 1: Nana's Chocolate Milk Recipe Video

  • The video is Act 1 of a3-Act Math Task developed by Dan Meyer.

Journal Prompt and Sample Response

1)How would you fix the drink so that Nana would be happy?

I would add 3 more scoops of chocolate and 1 more cup of milk for a total of 8 scoops of chocolate to 2 cups of milk.

2)How would you fix the drink if the glass holds less than 2 cups of milk?
I would add 1 more scoop of chocolate and ½ cup of milk for a total of 6 scoops of chocolate to 1.5 cups of milk.

3)How would you fix the drink if you have no chocolate mix left?
I would add ¼ cup of milk to the mixture for a total of 5 scoops of chocolate to 1.25 cups of milk.

Action

Task 2: Nana's Chocolate Milk Solution Video

  • A ratio table is used to solve Nana’s chocolate milk dilemma.

Journal Prompt and Sample Response

From the video, make notes about how to use a ratio table to solveNana's Chocolate Milk Dilemma.

  • Set up a ratio table and enter the original ratio given in the question.
  • Multiply or divide each term of the original ratio by the same number to get values that are in the same proportion as the original ratio.

Task 3: Did You Know?

  • Students read “Right Diagnosis” fromHealthgradesthat gives detailed information about deaths and adverse events due to errors in determining dosages of medication.
  • Students use ratio tables to solve three questions regarding dosages of medication and check their solutions with the sample ones provided.
  • Extend the questions by using a dosage that does not have an integral unit rate (e.g., 1000 mg over 3 days).

Consolidation

Task 4:Check Your Understanding

  • Students will:
  • solve three proportion problems
  • check their answer with the feedback provided
  • Can be a whole-class activity creating anAnchor Charton equivalent ratios for solving proportions using a ratio table.

Task 5: Discussion Prompts and Notes

  • Update your Frayer Model on proportional reasoning from Unit 4 Activity 1 with new information from this activity.
  • Describe how using a ratio table can be used to solve proportional problems.
  • Responses may include:
  • Ican make equivalent ratios by multiplying or dividing both terms of a given ratio by the same number.

Task 6:Assignment 1: Solving Ratio Problems Using a Ratio Table

  • Posted with unit.
  • See sample solution in the Teacher Notes posted on the vLE.

Task 7: Student Reflection

  • Students are asked to reflect on their understanding of this topic.
  • These reflections can be used as assessment for learning to help determine next steps for individual students.

Grade 9 Applied Blended Learning: Unit 4Activity 3 Page 1 of 3