## Sixth Grade Math for Parents

**Overview**

In sixth grade different number and arithmetic concepts come together and are used in interesting ways. Students are going to use their knowledge of multiplication and division to understand problems involving ratios and proportions. They’ll increase their skill with fractions to include dividing fractions. And they’ll begin to use equations and expressions with variables. Along the way, they’ll also fill in the number line with one more type of number as they begin to understand and work with negative numbers.

These topics are all highly interrelated. Students will use tables, graphs, number lines, and diagrams to represent a situation with ratios as different approaches to problem solving and to highlight different structure. For example, suppose a juice blend uses 5 cups of grape juice for every 2 cups of peach juice. A student could use a table to find “easy” combinations of peach and grape juice like 10 cups of grape juice and 4 cups of peach juice, then 15 cups and 6 cups, etc. noticing that each time the amount of grape juice increased by 5 while the peach juice increased by 2. Graphing these pairs on a coordinate plane would show further structure and prompt further insights.

The standard approach of “cross multiplying” will be a natural result of a solid understanding of the meaning of ratios in 7th grade. Finding the unit rate for ratios involving fractions will add a further context for fraction division then as well.

**Parent Tips**

- Be patient if your child struggles, especially if math has been relatively easy in the past. Make sure to emphasize that this struggle is not an indication of failure and mistakes are just opportunities to learn (see Carol Dweck’s work on mindset).

- Continue to have your child practice math as it comes up in your everyday interactions. (e.g. If it’s taken us 3 hours to get two thirds of the way to the cabin, how long do you expect the whole trip will take? If I get 2 pairs of pants and 3 shirts will I have enough money?)

- Because middle school begins a transition to more realistic modeling situations, ask your child to notice assumptions you make to solve everyday problems with math. For example, if 6 oz cost $3.25, how much will 15 oz. cost? Multiplying the cost by 2 ½ assumes that you
*can*purchase 15 oz, and that the unit price is the same for larger quantities.

From Bevans and Sinha, University of Oregon Department of Mathematics, October 2014