In grade six, different number and arithmetic concepts come together and are used in interesting ways. Students 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 another 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 might produce the following table:
Using this they might be able to figure out how many cups of grape juice for 7 cups of peach juice. Graphing these pairs on a coordinate plane would show further structure, such as seeing 2.5 cups of grape juice for every cup of peach juice, and prompt further insights.
Geometry in this grade provides opportunities for students to reason about formulas for length, area and volume, using both whole and fractional lengths. This will reinforce their work with equations and expressions, which are new in this grade. At this level, a wide range of applications to real life situations occur within geometry.
Statistical investigations will have students posing questions, collecting data, analyzing the data, and interpreting the results. They will compare data distributions by using what they know about measures of center and spread.