# Scaling Ratios to Solve Proportions | Ratios & Rates Visual Number Talk Prompts

This set of visual number talk prompts is taken from the number talk section of Day 2 in the Make Math Moments Problem Based Unit called Stacking Paper! (https://learn.makemathmoments.com/task/stacking-paper-day2).

All Math Is Visual number talk Prompts are useful for introducing and/or reinforcing mathematics concepts and skills to build fluency and flexibility with numbers and conceptualizing mathematics. While we suggest using these prompts at the beginning of a math lesson, they could be useful at any point during a math block as well as at home to strengthen (and excite) your child mathematically.

Students will engage in a visual number talk using geometric patterns to develop a deeper understanding of the following big ideas.

There are two types of ratios; composed unit and multiplicative comparison;
Thinking of a ratio as a multiplicative comparison involves describing
a quantity as “a number of times greater than another” or describing a quantity as “a fractional part of another” and often (not always) involves a ratio comparing quantities with the same units;
Ratios can be scaled in tandem to reveal an infinite number of equivalent ratios;
Although all ratios can be scaled in tandem, ratios thought of as a composed unit lend themselves more naturally to scaling;
Quotative division is applied when trying to determine a scale factor between two quantities/measures of the same unit (i.e. packs of paper and packs of paper, height and height);
Scaling ratios in tandem is thought of as a type of ratio reasoning;
An equation of two equivalent ratios is known as a proportion;
An unknown quantity from a proportion of equivalent ratios can be found by using quotative division to reveal a scale factor between two corresponding known quantities from both ratios;
A variety of mathematical models can be used as a tool for solving problems involving a proportional relationship and as a way to represent or prove your thinking. Some of these mathematical models include double bar/double number line models, ratio tables, two variable graphs, and equations;
The graph of a proportional relationship is linear and crosses through the origin, (0, 0); and,
The graph is helpful for identifying a trend or relationship between variable quantities and can be helpful when seeking to approximate the value of unknown quantities in that trend and/or relationship.

Notice the “PAUSE” prompts throughout which provide appropriate points to stop the video and give students time to think through their approaches using mathematical models as a means to see their strategies through.

To get the full breakdown of this Visual number talk Prompt Set, head to: https://mathisvisual.com/scaling-ratios-to-solve-proportions

To learn how to use Visual Number Talk Prompts:

How To Use Math Is Visual

To access the full problem based unit that this Number Talk was pulled from:

Stacking Paper [Day 2] – How Tall Is The Building?

To join the Make Math Moments Academy: