Number Sense & Number Theory

Tools for problem-solving, including estimation, rounding

Constants and variables

Bases, powers and exponents

Divisibility patterns

Prime and composite numbers

Estimating and Rounding

Classifying and organizing data into charts

Carrying out computation using the proper Order of Operations

Raising numbers to powers

Prime factorization

Given a 6-digit number, students must decide whether or not 2, 3, 4, 5, 6, 9 & 10 go into that number evenly (without using a calculator)

Given a pair of numbers, find both their greatest common factor and lowest common multiple

Fractions & Decimals

Operations with decimals and fractions

Review fraction operations, including division of fractions

Multiply and divide fractions, including mixed numbers and improper fractions.

Comparing and ordering fractions and decimals

Converting fractions to decimals and vice-versa

Conversion within the metric system using decimals

Division using decimals & rounding off answers to a given place value

Demonstrate the difference between division using remainders and division using decimals, then show why the two answers are equivalent

Show how fractions and decimals are different ways of expressing the same relationship

Chapter test on all related skills

Statistics

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Intro to Geometry

Measurement

Protractors and compasses, Angle measurement and relationships between angles and sides

Perimeter & circumference

Examine relationships between 2 parallel lines and angles formed by their transversal.

Perpendicular lines

Patterns in regular polygons

Collecting data & organizing it into a chart and/or frequency table

Find the scale, range mean, median and mode of a given set of data.

Read and interpret line plots and stem-and-leaf plots

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Acquire basic vocabulary of geometry to help discussion of angles, shapes and measurement

Measure angles of all sizes, including interior and exterior angles

Measure sides of a shape to find the perimeter.

Estimate circumference based on given diameter or radius

 

Using a given set of data, find the range, mode, median & mean and describe the significance of each of these

Area

Squares and square roots

Pythagorean Theorem

Area of rectangles, triangles, parallelograms, trapezoids and circles

Area of irregular figures

Squaring numbers by hand and using a calculator to find square roots.

Estimating square roots of numbers that are not perfect squares

Determining area of rectangles, triangles, parallelograms, trapezoids and circles

Estimating area of irregular figures

Given any two sides of a right angle triangle, find the third side

Given a variety of polygons, gather necessary info and find area of all shapes, applying formulas (calculators are allowed)

Surface Area & Volume

Surface area

3-dimensional shapes

Properties of prisms

Volume

Create outlines of 3 dimensional shapes on graph paper

Find surface area of rectangular and triangular prisms, as well as cylinders.

Find volume of rectangular and triangular prisms, as well as cylinders.

Create outlines of 3 dimensional shapes on graph paper and determine their surface area

Given a flat sheet of paper with given measurements, cut the corners to make an open-topped box. To score big, maximize the volume of the box, given the constraints of the single sheet of paper.

Ratio, Proportion & Percent

Ratio

Rates

Proportion

Percent

Conversion between fractions, decimals & percent

 

Determining if two ratio form a proportion or not

Discovering the value of the fourth quantity in a proportion containing a variable

 

Chapter test on all related topics

Career game activities to simulate many uses of percent in personal finance.

Applications of Percent

Percent of change

Simple and compound interest

Solving the percent proportion

Finding the percent of a number

Solving problems involving discounts, markups, tips and sales tax.

Probability & Discrete Math

Tree diagrams

Systematic Lists

Theoretical and experimental probability

Counting principle

Permutations

Combinations

Finding the probability of simple events

Finding the probability of consecutive events

Area models and probability

Counting using the multiplication rule

Finding the number of permutations or arrangements for a given list of items

Finding the number of combinations or groupings when selecting a set amount from a larger list of candidates

Given a sequence of three independent events, (coin flip & roll of 2 dice) what is the probability of all three turning out a certain way.

The dinner special at the local restaurant allows you to choose one appetizer from a list of 3 options, one entree out of four possibilities and one of two possible desserts. How many different possible "meals" could be ordered? Back up your guess with a systematic list and a tree diagram.

Integers, Equations & Graphing

E quations in one variable

Equations in two variables

The Language of Algebra

Variables as unknowns

Variables used to generalize symbolic rules and formulas

Sequences

Iterative and explicit patterns

Comparing and ordering integers

Reading and plotting points on the coordinate plane

Adding, subtracting, multiplying and dividing integers

Solving equations using inverse operations, including two-step equations

Writing algebraic expressions and equations to model real life relationships in word problems.

Graphing equations in two-variables on the coordinate plane

Practice using formulas by converting units within the customary or standard system.

 

Given a set of data, plot the points on the coordinate plane. Using a graphing calculator and trial and error, find the equation that best fits the data.

Given a story problem relating two sets of data, write the symbolic rule (equation) that shows that relationship.

Given an arithmetic sequence, find the 5th, 10th and 100th terms in the sequence and give the symbolic rule for the nth term in the sequence

Additional
Topics

need more hands-on work with basic measurement, metric system and conversion

tessellations

similar polygons