Mountainside Middle School # Home

Mathematics:

In grade seven, students will further develop their understanding of rates and ratios, using tables, graphs, and equations to solve real-world problems involving proportional relationships. Students will also work on quickly and accurately solving multi-step problems involving positive and negative rational numbers—any number that can be made by dividing one integer by another, such as ½, 0.75, or 2. Additionally, students will expand their knowledge of geometry and apply the properties of operations to solve real world problems involving the measurement of multi-dimensional objects. Activities in these areas will include:

Determining whether two quantities are in a proportional relationship and using knowledge of rates, ratios, proportions, and percentages to solve multi-step problems
Identifying the unit rate of change (the constant rate at which the value of a variable changes) in tables, graphs, equations, and verbal descriptions
Calculating the unit rates associated with ratios of fractions, including quantities measured in different units (for example, the ratio of ½ a mile for every ¼ of an hour means that you travel 2 miles in an hour)
Solving problems using equations to find the value of one missing variable
Applying the properties of operations to generate equivalent mathematical expressions
Solving multi-step word problems by adding, subtracting, multiplying, and dividing positive and negative rational numbers in any form (including whole numbers, fractions, or decimals)
Understanding that numbers cannot be divided by 0
Converting rational numbers to decimals using long division
Describing situations in which positive and negative quantities combine to make 0
Finding the area of two-dimensional objects and the volume and surface area of three-dimensional objects
CCSS Mathematics focus for 7th Grade

In grade eight, students take their understanding of unit rates and proportional relationships to a new level, connecting these concepts to points on a line and ultimately using them to solve linear equations that require them to apply algebraic reasoning as well as knowledge of the properties of operations. Students will also expand their understanding of numbers beyond rational numbers to include numbers that are irrational—meaning that they cannot be written as a simple fraction, such as the square root of 2 or √2 . Activities in these areas will include:

Understanding that every rational number (such as ½, 0.3, 2, or -2) can be written as a decimal, but that the decimal form of an irrational number (such as √2 ) is both non-repeating and infinite
Applying the properties of exponents to generate equivalent numerical expressions
Determining the value of square roots of small perfect squares (such as √49= 7) and cube roots of small perfect cubes (such as ³√64=4)
Graphing proportional relationships and interpreting the unit rate as the slope (how steep or flat a line is)
Solving and graphing one- and two-variable linear equations
Understanding that a function is a rule that assigns to each value of x exactly one value of y, such as y=2x, a rule that would yield such ordered pairs as (-2,-4), (3,6), and (4,8)
Comparing the properties of two functions represented in different ways (in a table, graph, equation, or description)
Determining congruence (when shapes are of equal size and shape) and similarity (same shape but different sizes)
Learning and applying the Pythagorean Theorem (an equation relating the lengths of the sides of a right triangle: a2 + b2 = c2)
Solving problems involving the volume of cylinders, cones, and spheres