Grade 7 Math

 Students will develop understanding of and apply proportional relationships.

2.     Students will develop understanding of operations with rational numbers and work with expressions and linear equations.

3.     Students will solve problems involving scale drawings and informal geometrical constructions, and work with two-and three-dimensional shapes to solve problems involving area, surface area, and volume.

4.     Students will draw inferences about populations bases on samples.

Doing More Math at Home

Two important goals for all students are that 1) they learn to value mathematics and 2) they become confident in their ability to do mathematics. Parents can help children develop a "can do" disposition toward math, by nurturing their children's natural curiosity and providing support and encouragement.

Math is everywhere, yet many children don't see it. Look for ways to point out and reinforce math skills at home. For example:

·        talk about how you use math at work or in the home

·        involve children in tasks that require computing, measuring, estimating, building, following directions, problem solving and reasoning

·        look for activities that require children to use their math skills such as building scale models, cooking, planning trips, and playing logic games

Look for games and activities that teach and/or reinforce math and thinking. For example, look for games that:

require and develop skill with mental computation and estimation

·        require players to use their math skills

·        involve the development of strategies

·        require players to think about the probability of certain events occurring

·        require the use of spatial visualization skills

·        require logical thinking

When you see articles that have data that might interest your children (e.g., sports statistics, data on teenage smoking, facts about natural disasters), share them and talk about what the numbers mean.

Share your problem-solving strategies and techniques, mental computation strategies, and estimation strategies. Have your children teach you some. Work on the same problem, and then compare strategies as well as answers.

Invite your children to explain what was learned in math class or have them teach it to you. It provides an opportunity for children to help clarify their thinking, to practice new skills, and to practice communicating mathematically.

If your children have access to technology, look for software and apps that reinforce and teach math concepts. Help your children learn to use math utilities such as spreadsheets and graphing programs.

Grade 7 Overview

Ratio and Proportional Relationships

·        Analyze proportional relationships and use them to solve real-world and mathematical problems.

·        Vocabulary

o   Commission – the amount earned, based on the percent of total sales.

o   Constant of proportionality – the constant ration of 2 proportional quantities, x and y; usually written as y =kx, where is k is the constant of proportionality.

o   Proportion - an equation stating that 2 ratios are equal. Ex.  =

o   Markup = the amount added to the buying price of an item.

o   Rate – a comparison of quantities in two different units is called a rate.  Ex. 20 cookies for 5 children or

o   Rate table – a table that shows the value of a single item in terms of another item.

o   Ratio – a comparison of two quantities and can be expressed as 3:5; 3 to 5; or

o   Unit rate – a rate in which one of the numbers is 1

o   Equivalent ratios – ratios whose fraction representations are equal.

o   Scale factor – number used to multiply the lengths of a figure to stretch or shrink it to a similar image.

The Number System

·        Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

·        Vocabulary

o   Absolute value – the distance a number is from 0 on a number line.

o   Integers – whole numbers and their opposites.

o   Negative number – A number less than 0.

o   Rational number – number that can be expressed as a quotient of two integers where the divisor is not 0.

o   Multiplicative identity – multiplying any rational number by 1 will the original number.

o   Multiplicative inverse – two numbers, a and b, that satisfy the equation ab = 1.

o   Opposites – two numbers whose sum is 0.  Ex. – 3 + 3 = 0

Expressions and Equations

·        Use properties of operations to generate equivalent expressions.

·        Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

·        Vocabulary

o   Distributive Property – a mathematical property used to rewrite expressions involving addition and multiplication.  EX. 4(5 + x) = 4(5) + 4(x) = 20 + 4x

o   Order of Operations – a set agreement for carrying out calculations with one or more operations. ( Parenthesis, Exponents, Multiplication/division (moving left to right), addition/subtraction (moving left to right)

o   Inequality –A statement that compares two quantities.  <, >, <, and > are used to express inequalities.

o   Variable – a quantity that can change, often represented by a letter

o   Coefficient – a number that is multiplied by a variable in an equation or expression.

o   Commutative property – property that states the order in which quantities are multiplied doesn’t change the product.

o   Slope – the number used to express the steepness of a line. 

o   Linear relationship – a relationship in which these is a constant rate of change between variables.

o   Dependent variable – It’s value depends upon or is determined by other variable.

o   Independent variable – It’s value determines the value of another variable.

Geometry

·        Draw, construct, and describe geometrical figures and describe relationships between them.

·        Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

·        Vocabulary

o   Circumference – the distance around a circle (perimeter)

o   Diameter – segment that goes from one point on a circle through the center to another point on the circle.

o   Radius – segment from the center of the circle to a point on the circle  (half the diameter)

o   Sphere – a three dimensional shape whose surface consists of all the points that are a given distance from the center of the shape.

o   Pyramid – a three dimensional shape with one polygonal base and lateral sides that are all triangles that meet at a vertex opposite the base.

o   Adjacent sides – two sides that meet at a vertex.

o   Corresponding sides – sides have same relative position in similar figures.

Statistics and Probability

·        Use random sampling to draw inferences about population.

·        Draw informal comparative inferences about two populations.

·        Investigate chance processes and develop, use and evaluate probability models.

·        Vocabulary

o   Compound event – consists of two or more simple events.

o   Favorable outcome – gives a desired result

o   Probability – a number between 0 and 1 that describes the likelihood that an outcome will occur.

o   Relative frequency – ratio of the number of desired results to the total number of trials.

o   Sample space – set of all possible outcomes in a probability solution.

o   Frequency – number of times a given data value occurs.

o   Distribution – entire set of collected data values, organized to show their frequency of occurrence.