Middle School Mathematics
The Hebrew Day middle school math program utilizes Imagine Illustrative Mathematics (Imagine IM). Imagine Illustrative Mathematics (Imagine IM) is a problem-based curriculum that fosters the development of mathematics learning communities in classrooms, gives students access to the mathematics through a coherent progression, and provides teachers the opportunity to deepen their knowledge of mathematics, students’ thinking, and their own teaching practice.
6th Grade Course
Grade 6 is a year of exciting mathematics. Students study ratio and rate, learn to divide fractions by fractions, extend their understanding of number to include negative numbers, and understand and use variables, to name just some of the major work of this year.
IM Grade 6 begins with an exploration of area and surface area—an invitation for students to engage with novel ideas that they can represent concretely and visually, and reason about in intuitive ways. Starting with geometry also creates opportunities to elicit close observation, sense- and connection-making, and the exchange of ideas—elements of a healthy learning community.
The next two units introduce ratios and rates, concepts that are also new. Students learn to represent, make sense of, and solve problems about equivalent ratios, rates, unit rates, and percentages. The mathematical reasoning here constitutes major work of the grade.
In the two units that follow, students expand and deepen their prior knowledge of numbers and operations. In one unit, students explore division involving fractions, and work toward dividing a fraction by fraction. In the other, they learn to multiply and divide multi-digit, base-ten numbers, including decimals, using the standard algorithm for each operation. Building fluency with algorithms takes time and continues beyond the two units.
Next, students further their understanding of equations and expressions, including those with variables. Students consider ways to represent, justify, and generate equivalent expressions. They also use expressions and equations to describe the relationship between quantities.
From there, students are introduced to rational numbers. Students learn about negative numbers, and represent negative numbers on the number line and on the coordinate plane. They analyze and write inequalities that compare rational numbers.
Toward the end of the course, students examine data sets and distribution. They learn about statistical questions, categorical data, and numerical data. They also explore ways to describe the centers and the distribution of a data set.
7th Grade Course
Welcome to Grade 7 mathematics, a critical year when students extend concepts of rates and ratios to work with equivalent ratios and proportional relationships. Students expand their understanding of fractions to include all rational numbers and become comfortable working with and comparing expressions and equations. Throughout it all, students solve compelling mathematical and real world problems.
IM Grade 7 begins with students studying scale drawings, an engaging geometric topic that sets the stage for the subsequent work on proportional relationships in the following three units. Students also have opportunities to build fluency with IM Grade 6 arithmetic. They work with proportional relationships represented by tables, equations, and graphs. Geometry and proportional relationships are interwoven in the third unit, when the important proportional relationship between a circle's circumference and its diameter is studied. Then students work with percent increase and percent decrease.
By the fifth unit, on operations with rational numbers, students have had time to brush up on and solidify their understanding of, and skill in, IM Grade 6 arithmetic. At this point, the emphasis becomes the role of the properties of operations in determining the rules for operating with negative numbers. This is a natural lead-in to the work on solving equations and simplifying expressions in the next unit. Students then put their arithmetical and algebraic skills to work in the last two units: on angles, triangles, and prisms, and on probability and sampling.
8th Grade Course
In this course, eighth graders tackle exciting new ideas and concepts in preparation for work in high school. They extend earlier understandings of proportional relationships to study linear relationships and work with linear equations in one and two variables. Among other things, they are also introduced to the idea of functions and have their first encounter with irrational numbers.
IM Grade 8 begins with transformational geometry. Students study rigid transformations and congruence, and then dilations and similarity. This provides background for understanding the slope of a line in the coordinate plane.
Next, students build on their understanding of proportional relationships, from IM Grade 7, to study linear relationships. They use equations, tables, and graphs to represent linear relationships, and make connections across these representations. Students expand their ability to work with linear equations in one and two variables, extending their understanding of a solution to an equation in one or two variables to comprehend a solution to a system of equations in two variables. They learn that linear relationships are an example of a special kind of relationship called a function. Students apply their understanding of linear relationships and functions to contexts involving data with variability.
The course ends the year with students extending their understanding of exponents to include all integers, and in the process codifying the properties of exponents. They learn about orders of magnitude and scientific notation in order to represent and compute with very large and very small quantities. They encounter irrational numbers for the first time and informally extend the rational-number system to the real-number system, motivated by their work with the Pythagorean Theorem.