This year we will be using Illustrative Math for 7th grade and completing most of our work on the Imagine Learning online platform. Links to new unit information will be posted here when appropriate, and daily assignments will be linked through Google Classroom.
Embedded Files
Unit One: Scale Drawings
In this unit, students study scaled copies of plane figures and scale drawings of real-world objects. Students learn that all lengths in a scaled copy are the result of multiplying the original lengths by a scale factor. Also, the angle measures in a scaled copy are the same as in the original figure.
This work builds on what students learned in previous grades about measuring lengths, areas, and angles. This unit provides a geometric context to preview the type of reasoning that students will use with proportional relationships later in grade 7. It also lays the foundation for grade 8 work on dilations and similarity.
Students begin the unit by looking at copies of a picture and describing what differentiates scaled and non-scaled copies. They calculate scale factors and draw scaled copies of figures. Note that the study of scaled copies is limited to pairs of figures that have the same orientation — in other words, they are not rotations or reflections of each other. In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reflections, and dilations.
Next, students study scale drawings. They see that the principles and strategies that they used to reason about scaled copies of figures can also be used with scale drawings. They use scale drawings to calculate actual lengths and areas, and they create scale drawings.
Unit Two: Introducing Proportional Relationships
In this unit, students develop the idea of a proportional relationship. They work with proportional relationships that are represented in tables, as equations, and on graphs. This builds on grade 6 work with equivalent ratios and helps prepare students for the study of linear functions in grade 8.
Students begin by looking at tables. In a table of equivalent ratios, a multiplicative relationship between a pair of rows is given by a scale factor, while the multiplicative relationship between the columns is given by a unit rate. Students learn that the relationship between pairs of values in the two columns is called a "proportional relationship," and the unit rate that describes this relationship is called a "constant of proportionality."
Next, students use equations of the form to represent proportional relationships and solve problems. They determine whether given tables and equations could represent a proportional relationship.
Then students investigate graphs of proportional relationships. They recognize that the graph of a proportional relationship is a straight line through . They interpret points on the graph, including the point . Here is an example of a graph, an equation, and a table that all represent the same proportional relationship.
By the end of the unit, students should be comfortable working with common contexts associated with proportional relationships (such as constant speed, unit pricing, and measurement conversions) and be able to determine whether or not a relationship is proportional. In a later unit, students will apply proportional reasoning to solve multi-step problems and to calculate more complex rates.
Unit Four: Proportional Relationships & Percentages
Unit Five: Rational Number Arithmetic
Unit Six: Expressions, Equations & Inequalities
Unit Eight: Probability & Sampling
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