## Topic outline

- General
### General

**Course Description**This course is designed to formalize and extend the mathematics that students learned in elementary school. Students connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems. Students formalize an understanding of division of fractions and extend their learning to the system of rational numbers, including ordering and comparing negative numbers. Students develop their algebraic thinking through writing, interpreting, and using expressions and equations. Students develop an understanding of statistical thinking. Throughout this course, students will persevere in problem solving, engage in mathematical arguments, model mathematics, communicate with precision, discern patterns and structures, and analyze the whole situation and work with the details. Students will utilize both content and practice in the context of real world situations.

Key Course Learning Experiences

(example is for 6th grade, descriptions adapted from the Unit narrative)

Area and Surface Area

Students reason with parallelograms, rectangles, triangles to find area and polyhedra with triangular and rectangular faces to find surface area.

Introducing Ratios

Students use tables and double number lines to reason with equivalent ratios and rates.

Unit Rates and Percentages

Students reason with unit rate and connect percentages to equivalent ratios and rates per 100.

Dividing Fractions

Students make an explicit connection between multiplication and division. Students use their understanding of whole number division and tape diagrams to compute quotients of fractions. Students apply their understanding of area and volume to figures with fractional side lengths.

Arithmetic in Base Ten

Students extend their understanding of addition, subtraction, and multiplication of whole numbers to decimal numbers. Students develop an efficient process to divide whole numbers and decimals.

Expressions and Equations

Students represent relationships between quantities with tape diagrams and equations. Students solve linear equations in one variable using hanger diagrams and model linear expressions with area diagrams. Students apply the distributive property to write equivalent expressions.

Rational Numbers

Students compare the magnitude (absolute value) and order (position on number line) of two signed numbers. Students graph inequalities in one variable on a number line.

Data Sets and Distributions

Students learn about populations and study variables associated with a population. Students make and interpret histograms, bar graphs, tables of frequencies, and box plots. Students work with measures of center and measures of variability.

**Essential Learning Goals**1. Attends to precision (40%)

Work shown displays the correct procedures to solve problems.

2. Problem Solving (40%)

Apply and adapt a variety of appropriate strategies to solve problems.

3. Communication (20%)

Coherently communicates mathematical thinking both spoken and written.

**Major Assessments and Success Criteria**Students will engage in formative practices, summative assessments, and performance tasks employing the Essential Learning Goals as applied to proportional reasoning, rational numbers, algebraic reasoning, and statistical thinking. Through a process of reflection and revision, students will work towards mastery of his/her learning. Assessments will be multifaceted with an emphasis on skills that will enhance their upper level math thinking, and will relate mathematics to the real world.