 1.     Students will connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems.

2.     Students will complete understanding of division of fractions and extend the notion of number to the system of rational numbers, which includes negative numbers.

3.     Students will write, interpret, and use expressions and equations.

4.     Students will develop an understanding of statistical thinking.

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.

Ratio and Proportional Relationships

·        Understand ratio concepts and use ratio reasoning to solve problems.

·        Vocabulary

o   Ratio – a comparison of 2 quantities expressed as 3/5, 3:5, or 3 to 5.

o   Unit rate – a rate with one of the numbers is 1 or a quantity of 1.

o   Percent – out of 100.

o   Income – amount of money taken in.

o   Profit – amount by which income is greater than expenses.

The Number System

·        Apply and extend previous understandings of multiplication and division to divide fractions by fractions

·        Multiply and divide multi-digit numbers and find common factors and multiples.

·        Apply and extend previous understandings of numbers to the system of rational numbers.

·        Vocabulary

o   Factor – one or more whole numbers that are multiplied together to get a product.

o   Multiple – the product of a given whole number and another whole number.

o   Prime – a number with exactly two factors, one and itself.

o   Composite – a number with more than two factors.

o   Prime factorization – a product of prime numbers, perhaps with some repetitions, resulting in the desired number. EX. 27 = 3 x 3 x 3 or 30 = 2 x 3 x 5

o   Square number – a number that is the result of the product of a number multiplied by itself.

o   Least common multiple (LCM) – the least multiple that two or more numbers share.

o   Greatest common factor (GCF) – greatest factor that two or more numbers share.

o   Exponent – the small raised number that tells how many times a factor is used.

o   Repeating decimal – a decimal with a pattern of a fixed number of digits that repeats forever.

o   Terminating decimal – a decimal that ends or terminates.

Expressions and Equations

·        Apply and extend previous understandings of arithmetic to algebraic expressions.

·        Reason about and solve one-variable equations and expressions.

·        Represent and analyze quantitative relationships between dependent and independent variables.

·        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   Equivalent – equal in value

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

o   Expression – a mathematical phrase containing numbers, variables, and operation symbols.

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.

Geometry

·        Solve real-world and mathematical problems involving area, surface area, and volume.

·        Vocabulary

o   Area – measure of the amount of surface enclosed by the boundary of a figure, amount of square units in a figure.

o   Perimeter – the measure of the distance around a two-dimensional figure.

o   Volume – the amount of space occupied by a three-dimensional shape, number of unit cubes that fit into shape.

o   Surface area – area required to cover a three-dimensional shape.

o   X and Y coordinates – numbers in a coordinate pair used to locate a point on a coordinate graph.

Statistics and Probability

·        Develop understanding of statistical variability.

·        Summarize and describe distributions.

·        Vocabulary

o   Mean – value found when all the data are combined and then redistributed evenly (the average)

o   Median – the number that is the midpoint of an ordered set of data.

o   Mode – number that appears the most in a given set of data.

o   Range – difference between the maximum value and the minimum value in a distribution.

o   Line plot – a way to organize data along a number line where X (or other symbols) above a number represent how often each value is mentioned.

o   Frequency table -

o   Box plot – a dis play that shows distribution of values in a data set separated into 4 equal size groups, constructed from a 5 numbers summary of data (minimum value, lower quartile, median, upper quartile, and maximum value)

o   Upper quartile – the median of the data to the left of the median.

o   Lower quartile – the median of the data to the right of the median.

o   Outlier - a value that lies far from the center of a distribution of data and is not like the other values.