Unit 3: Measuring Circles
In this unit, students extend their knowledge of circles and geometric measurement, applying their knowledge of proportional relationships to the study of circles. They extend their grade 6 work with perimeters of polygons to circumferences of circles, and recognize that the circumference of a circle is proportional to its diameter, with constant of proportionality π. They encounter informal derivations of the relationship between area, circumference, and radius.
Unit 4: Proportional Relationships and Percents
Dates: November - December
Students began their work with ratios, rates, and unit rates in grade 6, representing them with expressions, tape diagrams, double number line diagrams, and tables. They used these to reason about situations involving color mixtures, recipes, unit price, discounts, constant speed, and measurement conversions. They extended their understanding of rates to include percentages as rates per 100, reasoning about situations involving whole-number percentages. They did not use the terms “proportion” and “proportional relationship” in grade 6.
Unit 5: Rational Number Arithmetic
Dates: January -February
In grade 6, students learned that the rational numbers comprise positive and negative fractions. They plotted rational numbers on the number line and plotted pairs of rational numbers in the coordinate plane. In this unit, students extend the operations of addition, subtraction, multiplication, and division from fractions to all rational numbers, written as decimals or in the form ab.
Unit 6: Expressions, Equations, and Inequalities
Dates: February - March
In this unit, students solve equations of the forms px+q=r and p(x+q)=r, and solve related inequalities, e.g., those of the form px+q>rand px+q≥r, where p, q, and r are rational numbers.
Unit 7: Angles, Triangles, and Prisms
Dates: March - April
In this unit, students investigate whether sets of angle and side length measurements determine unique triangles or multiple triangles, or fail to determine triangles. Students also study and apply angle relationships, learning to understand and use the terms “complementary,” “supplementary,” “vertical angles,” and “unique” . The work gives them practice working with rational numbers and equations for angle relationships. Students analyze and describe cross-sections of prisms, pyramids, and polyhedra. They understand and use the formula for the volume of a right rectangular prism, and solve problems involving area, surface area, and volume. Students should have access to their geometry toolkits so that they have an opportunity to select and use appropriate tools strategically.
Unit 8: Probability and Sampling
Dates: April - May
In this unit, students understand and use the terms “event,” “sample space,” “outcome,” “chance experiment,” “probability,” “simulation,” “random,” “sample,” “random sample,” “representative sample,” “overrepresented,” “underrepresented,” “population,” and “proportion.” They design and use simulations to estimate probabilities of outcomes of chance experiments and understand the probability of an outcome as its long-run relative frequency. They represent sample spaces (that is, all possible outcomes of a chance experiment) in tables and tree diagrams and as lists. They calculate the number of outcomes in a given sample space to find the probability of a given event. They consider the strengths and weaknesses of different methods for obtaining a representative sample from a given population. They generate samples from a given population, e.g., by drawing numbered papers from a bag and recording the numbers, and examine the distributions of the samples, comparing these to the distribution of the population. They compare two populations by comparing samples from each population.
Unit 1: Scale Drawings
Dates: August - September
In this unit, students study scaled copies of pictures and plane figures, then apply what they have learned to scale drawings, e.g., maps and floor plans. This provides geometric preparation for grade 7 work on proportional relationships as well as grade 8 work on dilations and similarity.
Unit 2: Introducing Proportional Relationships
Dates: September 23 - October
Students learn that any proportional relationship can be represented by an equation of the form y=kx where k is the constant of proportionality, that its graph lies on a line through the origin that passes through Quadrant I, and that the constant of proportionality indicates the steepness of the line. By the end of the unit, students should be able to easily work with common contexts associated with proportional relationships (such as constant speed, unit pricing, and measurement conversions) and be able to determine whether a relationship is proportional or not.