7th Grade Math

Period 1, 2, 4, 5

Unit 1: Integers

Calculators allowed: No

On the test I will show that ...

I can graph integers and their opposites on a number line.

I can compare and order integers.

I can add two or more integers to find the sum.

I can subtract two integers to find the difference.

I can multiply two integers to find the product.

I can divide two integers to find the quotient.

I can write and compute expressions with powers.

I can find the value of expressions using the order of operations. 

 Vocabulary to know:

• integer

• sum

• difference

• product

• quotient

• expression

• power

• order of operations

• absolute value

Free Online games:

Ordering Integers:  

Number Balls

Integers Game

Adding Integers:

Orbit Integers

Pirates 

Spider Match

Subtracting Integers:

Integer Subtraction

Racing Integer Subtraction

Multiply Integers:

Integer Multiplication

Speed Racing Integers

Integer Warp

Divide Integers:

Integer Warp Division

Number Balls Division

Fruit Shoot Division

Mixed Operations:

 Fruit Shoot Mixed Integers

Exponents and Powers

Otter Rush

Pirates Exponents

Unit 2: Fractions

 Calculators allowed: No

On the test I will show that ...

I can write fractions in simplest form. 

I can write mixed numbers as improper fractions. 

I can write improper fractions as mixed numbers. 

I can add and subtract fractions

I can multiply and divide fractions 

I can add, subtract, multiply or divide fractions

Vocabulary to know:

• mixed number

• improper fraction

• denominator

• numerator

• simplest form

Free online games to help practice fractions and integers: 

Fruit Shoot : simplifying, adding, subtracting

Speedway: adding fractions

Speedway: subtracting fractions

Snow Sprint : multiplying fractions

Fraction Millionaire : multiplying fractions

Soccer:  multiplying fractions

Basketball: dividing fractions

Moonshoot: dividing fractions

Orbit Integers adding integers

Pirates adding integers

Spider Match adding integers

Integer Subtraction subtracting integers

Racing Integer Subtraction subtracting integers

Integer Multiplication multiply integers

Speed Racing Integers multiply integers

Integer Warp multiply integers

Integer Warp Division divide integers

Number Balls Division divide integers

Fruit Shoot Division divide integers

Fruit Shoot Mixed Integers mixed operations

Unit 3: Solving Equations

Calculators allowed: Yes

On the test I will show that ...

I can write and evaluate algebraic expressions.

I can determine if a number is a solution of an equation.

I can use inverse operations to solve one-step equations. 

I can solve two-step equations.

I can use the Distributive Property to simplify expressions.

I can solve equations using the Distributive Property. 

I can simplify expressions using the Distributive Property and combining like terms.

I can simplify and solve equations with variables on one side of an equation. 

This is the only time work must be done "my" way:

1. Show work on both sides of the equation.

2. Use a fraction to represent division

3. Use a dot or parenthesis- not an x- to represent multiplication

4. Work shown straight down

Vocabulary to know:

• expression

• equation

• variable

• Distributive Property

• simplify

• evaluate (solve)

Unit 4: Two- Dimensional Geometry

Calculators allowed: Yes

FORMULAS to have memorized:

• Area of a Parallelogram:        A = bh

• Area of a Triangle:                  A = ½bh

• Area of a Trapezoid:               A = ½h(b1 + b2)

• Area of a Circle                       A = π r2

• Circumference of a Circle      C = 2 π r or C = π d 

On the test I will show that ...

I can use area formulas to compute areas of geometric shapes and find missing measures.

I can understand and use the trapezoid formula.

I can identify, name and define parts of a circle.

I can understand and use the relationship between pi and diameter to find circumference.

I can understand and use the circle area formula.

I can find the area of composite figures.

 Vocabulary to know:

• area 

• diameter

• radius

• circumference

• pi (as 3.14, 22/7, or π)

• composite figures

• trapezoid

• center (of a circle)

• chord

Unit 5: Rates and Ratios

Calculators allowed: Yes

On the test I will show that ...

I can convert customary and metric measurements.

I can convert fractions to decimals and decimals to fractions.

I can simplify and write ratios in three forms.

I can calculate unit rates.

I can convert rates to different units.

I can compute rates and ratios that include complex fractions.

Vocabulary to know:

• rate 

• ratio

• unit rate

• unit price

• cross multiplication 

• complex fraction

Conversions to know:

•  Metric: mm, cm, m, km

• Customary: in, ft, yds, mi

• Time: sec, min, hrs, days, wks, yrs

Unit 6: Proportions and Similarity

Calculators allowed: Yes

On the test I will show that ...

I can write and solve proportions.

I can solve problems by writing and solving proportions.

I can recognize congruent and similar figures.

I can find the scale factor of similar figures.

I can use proportions to solve problems involving similar figures.

I can find the scale factor, ratio of perimeters and ratio of areas of similar figures.

I can use scales for maps, blueprints and models to find missing measurements.

Vocabulary to know:

• proportion

• rate 

• scale 

• scale factor

• congruent

• corresponding

• similar

The four steps of solving ratios:

1.    Write the ratio in words

2.    Write the given ratio

3.    Fill in given information (or a 1 for unit rate/price) and calculate

4.    Write the answer (include label!)

Unit 7: Percents

Calculators allowed: Yes

On the test I will show that ...

I can convert between fractions, decimals and percents.

I can find the percent of a number using proportions.

I can find a missing number using proportions with percents.

I can find the percent of a number using the percent equation.

I can find a missing number using the percent equation.

I can find the percent of increase or the percent of decrease between two numbers.

I can use percent of change to find new values.  

Vocabulary to know:

• percent

• percent of change

• increase 

  • tip, tax, bonus, growth, more, mark-up, etc.

• decrease

  • discount, sale, loss, less, off, etc

Unit 8: Probability 

Calculators allowed: Yes

On the test I will show that ...

I can find and interpret experimental and theoretical probabilities.

I can predict an outcome using experimental and theoretical probability.

I can create and interpret pie charts and histograms.

Vocabulary to know:

• experimental probability

• theoretical probability

• event

• outcome

• P(event)

Mini Unit A: MMMR 

Calculators allowed: Yes

On the test I will show that ...

I can compare samples using measures of center and variability.

I know how to find Mean, Median, Mode, and Range

Vocabulary to know:

• Mean

• Median

• Mode

• Range

Unit 9: Proportional Relationships

Calculators allowed: Yes

On the test I will show that ...

I can recognize and graph ordered pairs on a coordinate plane.

I can recognize direct variation/proportional relationships  in tables and graphs.

 I can write and graph direct variation equations.

I can identify direct variation from other functions given graphs, tables or equations

Vocabulary to remember:

• equation

• coordinate grid/plane

• ordered pair (on coordinate plane)

• plot (points on a coordinate plane)

• rate of change

• proportional

Vocabulary to know:

• direct variation/proportional relationship

• point of origin (0,0)

• Function Rule

• Input/Output

• rate/rate of change/slope (on a coordinate plane)

Unit 10: Angle Relationships

Calculators allowed: Yes

On the test I will show that ...

I can measure, name and draw angles.

I can classify angles as acute, right, obtuse or straight.

I can use facts about complementary and supplementary angles to solve problems.

I can use facts about vertical and adjacent angles to solve problems.

Vocabulary to know:

• acute angle

• right angle

• obtuse angle

• straight angle

• complementary angles

• supplementary angles

• vertical angles

• adjacent angles

• linear angles

• Congruent

• similar

Unit 11: Three-Dimensional Unit

Calculators allowed: Yes

On the Surface Area Quiz I will show that ...

• I can identify the names and qualities of three-dimensional figures.

• I can sketch and draw solids in two dimensions and in three dimensions.

• I can calculate the surface area of prisms.

• I can calculate the surface area of pyramids.

On the Volume Quiz I will show that ...

• I can describe two-dimensional figures that result from slicing three-dimensional figures.

• I can calculate the volume of prisms.

• I can calculate the volume of pyramids.

Vocabulary to know:

• base (of 3D figure)

• face (of 3D figure)

• prism (identify full name using the base)

• pyramid (identify full name using the base)

• surface area

• volume

• parallel (to base of object)

• perpendicular (to base of object)

Formulas to know :

Surface area of a prims:  SA = Ph + 2B (optinal)

Surface area of a pyramid: SA = ½Ph + B (optinal)

Volume of a prism: V = Bh  

Volume of a pyramid: V = 1/3 Bh   

**B = area of base

Accelerated Math 

Period 6, 7

Unit 1: Integers

Calculators allowed: No

On the test I will show that ...

I can graph integers and their opposites on a number line.

I can compare and order integers.

I can add two or more integers to find the sum.

I can subtract two integers to find the difference.

I can multiply two integers to find the product.

I can divide two integers to find the quotient.

I can write and compute expressions with powers.

I can find the value of expressions using the order of operations. 

 Vocabulary to know:

• integer

• sum

• difference

• product

• quotient

• expression

• power

• order of operations

• absolute value

Free Online games:

Ordering Integers:  

Number Balls

Integers Game

Adding Integers:

Orbit Integers

Pirates 

Spider Match

Subtracting Integers:

Integer Subtraction

Racing Integer Subtraction

Multiply Integers:

Integer Multiplication

Speed Racing Integers

Integer Warp

Divide Integers:

Integer Warp Division

Number Balls Division

Fruit Shoot Division

Mixed Operations:

 Fruit Shoot Mixed Integers

Exponents and Powers

Otter Rush

Pirates Exponents

Unit 2: Fractions

 Calculators allowed: No

On the test I will show that ...

I can write fractions in simplest form. 

I can write mixed numbers as improper fractions. 

I can write improper fractions as mixed numbers. 

I can add and subtract fractions with positive and negative numbers

I can multiply and divide fractions with positive and negative numbers

I can add, subtract, multiply or divide mixed numbers with positive and negative numbers

Vocabulary to know:

• mixed number

• improper fraction

• denominator

• numerator

• simplest form

Free online games to help practice fractions and integers: 

Fruit Shoot : simplifying, adding, subtracting

Speedway: adding fractions

Speedway: subtracting fractions

Snow Sprint : multiplying fractions

Fraction Millionaire : multiplying fractions

Soccer:  multiplying fractions

Basketball: dividing fractions

Moonshoot: dividing fractions

Orbit Integers adding integers

Pirates adding integers

Spider Match adding integers

Integer Subtraction subtracting integers

Racing Integer Subtraction subtracting integers

Integer Multiplication multiply integers

Speed Racing Integers multiply integers

Integer Warp multiply integers

Integer Warp Division divide integers

Number Balls Division divide integers

Fruit Shoot Division divide integers

Fruit Shoot Mixed Integers mixed operations

Unit 3: Solving Equations

Calculators allowed: Yes

On the test I will show that ...

I can write and evaluate algebraic expressions.

I can determine if a number is a solution of an equation.

I can use inverse operations to solve one-step equations. 

I can solve two-step equations.

I can use the Distributive Property to simplify expressions.

I can solve equations using the Distributive Property. 

I can simplify expressions using the Distributive Property and combining like terms.

I can simplify and solve equations with variables on one side of an equation. 

I can simplify and solve equations with variables on both sides of an equation. ­­

This is the only time work must be done "my" way:

1. Show work on both sides of the equation.

2. Use a fraction to represent division

3. Use a dot or parenthesis- not an x- to represent multiplication

4. Work shown straight down

Vocabulary to know:

• expression

• equation

• variable

• Distributive Property

• simplify

• evaluate (solve)

Unit 4: Two- Dimensional Geometry

Calculators allowed: Yes

FORMULAS to have memorized:

• Area of a Parallelogram:        A = bh

• Area of a Triangle:                  A = ½bh

• Area of a Trapezoid:               A = ½h(b1 + b2)

• Area of a Circle                       A = π r2

• Circumference of a Circle      C = 2 π r or C = π d 

On the test I will show that ...

I can use area formulas to compute areas of geometric shapes and find missing measures.

I can understand and use the trapezoid formula.

I can identify, name and define parts of a circle.

I can understand and use the relationship between pi and diameter to find circumference.

I can understand and use the circle area formula.

I can find the area of composite figures.

 Vocabulary to know:

• area 

• diameter

• radius

• circumference

• pi (as 3.14, 22/7, or π)

• composite figures

• trapezoid

• center (of a circle)

• chord

Unit 5: Rates and Ratios

Calculators allowed: Yes

On the test I will show that ...

I can convert customary and metric measurements.

I can convert fractions to decimals and decimals to fractions.

I can simplify and write ratios in three forms.

I can calculate unit rates.

I can convert rates to different units.

I can compute rates and ratios that include complex fractions.

Vocabulary to know:

• rate 

• ratio

• unit rate

• unit price

• cross multiplication 

• complex fraction

Conversions to know:

•  Metric: mm, cm, m, km

• Customary: in, ft, yds, mi

• Time: sec, min, hrs, days, wks, yrs

Unit 6: Proportions and Similarity

Calculators allowed: Yes

On the test I will show that ...

I can write and solve proportions.

I can solve problems by writing and solving proportions.

I can recognize congruent and similar figures.

I can find the scale factor of similar figures.

I can use proportions to solve problems involving similar figures.

I can find the scale factor, ratio of perimeters and ratio of areas of similar figures.

I can use scales for maps, blueprints and models to find missing measurements.

Vocabulary to know:

• proportion

• rate 

• scale 

• scale factor

• congruent

• corresponding

• similar

The four steps of solving ratios:

1.    Write the ratio in words

2.    Write the given ratio

3.    Fill in given information (or a 1 for unit rate/price) and calculate

4.    Write the answer (include label!)

Unit 7: Percents

Calculators allowed: Yes

On the test I will show that ...

I can convert between fractions, decimals and percents.

I can find the percent of a number using proportions.

I can find a missing number using proportions with percents.

I can find the percent of a number using the percent equation.

I can find a missing number using the percent equation.

I can find the percent of increase or the percent of decrease between two numbers.

I can use percent of change to find new values.  

Vocabulary to know:

• percent

• percent of change

• increase 

  • tip, tax, bonus, growth, more, mark-up, etc.

• decrease

  • discount, sale, loss, less, off, etc

Unit 8: Probability 

Calculators allowed: Yes

On the test I will show that ...

I can find and interpret experimental and theoretical probabilities.

I can predict an outcome using experimental and theoretical probability.

I can create and interpret pie charts and histograms.

I can apply the concepts of compound probability 

Vocabulary to know:

• experimental probability

• theoretical probability

• event

• outcome

• P(event)

Mini Unit A: MMMR 

Calculators allowed: Yes

On the test I will show that ...

I can compare samples using measures of center and variability.

I know how to find Mean, Median, Mode, and Range

Vocabulary to know:

• Mean

• Median

• Mode

• Range

Unit 9: Linear Equations

Calculators allowed: Yes

On the test I will show that ...

I can recognize and graph ordered pairs on a coordinate plane.

I can recognize direct variation in tables and graphs.

 I can write and graph direct variation equations.

I can identify direct variation from other functions given graphs, tables or equations

I can find the slope of a line using the slope formula.

I can graph linear equations in slope-intercept form.

I can write a linear equation for a given graph.

Vocabulary to remember:

• • equation

  • coordinate grid/plane

  • ordered pair (on coordinate plane)

  • plot (points on a coordinate plane)

  • rate of change

Vocabulary to know:

• direct variation

• point of origin (0,0)

• Function Rule

• Input/Output

• rate (on a coordinate plane)

• Slope

• y-intercept

• linear equation

Unit 10: Angle & Triangles

Calculators allowed: Yes

On the test I will show that ...

I can measure, name and draw angles.

I can classify angles as acute, right, obtuse or straight.

I can use facts about complementary and supplementary angles to solve problems.

I can use facts about vertical and adjacent angles to solve problems.

I can recognize and apply properties of alternate exterior and alternate interior angles.

I can recognize and apply properties of corresponding and same-side interior angles.

I can classify triangles based on sides and angles.

I can find angle measures in a triangle.

I can find measures of angles in isosceles and equilateral triangles.

I can determine if triangles are similar or congruent and find the missing measure.

I can use special angle relationships to find angle measures.

Vocabulary to know:

• acute angle

• right angle

• obtuse angle

• straight angle

• complementary angles

• supplementary angles

• vertical angles

• adjacent angles

• linear angles

• congruent

• Similar

• corresponding parts, sides, angles

• alternate exterior angles

• alternate interior angles

• corresponding angles

• same-side interior angles

• transversal line

• acute, right, and obtuse triangles

• equilateral, scalene, and isosceles triangles

• equiangular triangles

Unit 11: Three-Dimensional Unit

Calculators allowed: Yes

On the Surface Area Quiz I will show that ...

• I can identify the names and qualities of three-dimensional figures.

• I can sketch and draw solids in two dimensions and in three dimensions.

• I can calculate the surface area of prisms.

• I can calculate the surface area of pyramids.

On the Volume Quiz I will show that ...

• I can describe two-dimensional figures that result from slicing three-dimensional figures.

• I can calculate the volume of prisms.

• I can calculate the volume of pyramids.

• I can find the volume of cylinders and solve real-world problems involving cylinders.

• I can find the volume of cones and solve real-world problems involving cones.

• I can find the volume of spheres and solve real-world problems involving spheres.

Vocabulary to know:

• base (of 3D figure)

• face (of 3D figure)

• prism (identify full name using the base)

• pyramid (identify full name using the base)

• surface area

• volume

• parallel (to base of object)

• perpendicular (to base of object)

Formulas to know :

Surface area of a prims:  SA = Ph + 2B (optinal)

Surface area of a pyramid: SA = ½Ph + B (optinal)

Volume of a prism: V = Bh  

Volume of a pyramid: V = 1/3 Bh   

Volume of a cylinder:  V = πr2h

Volume of a cone: V = ⅓πr2h

Volume of a sphere          V=(4 πr³)/3

**B = area of base

Unit 12: The Pythagorean Theorem Unit

Calculators allowed: Yes

On the test I will show that ...

I can recognize and find the values of perfect squares.

I can estimate the value of square roots.

I can use the Pythagorean Theorem to find the missing side lengths in right triangles. 

I can determine if three sides create a right triangle.

I can apply the Pythagorean Theorem to solve problems in two and three dimensions.

I can find the distance between two points on a coordinate plane using the Pythagorean Theorem.

I can find the distance between two points on a coordinate plane using the Distance Formula.

New Vocabulary:

• • • square root

    • perfect square root

    • hypotenuse

    • leg (of a triangle)

    • Pythagorean Theorem

    • converse of the Pythagorean Theorem

    • Pythagorean Theorem triples

Formulas to know:

• The Pythagorean Theorem:   a2 + b2 = c2 

• The Pythagorean Theorem in three dimensions:   a2 + b2 + c2 = d2

• The Distance Formula: (see your notes)

Unit 13: Exponents Unit

Calculators allowed: No

On the test I will show that...

4.1 I can simplify expressions using multiplication using properties of exponents.

4.2 I can use properties of exponents to simplify expression involving division.

4.3 I can express numbers in scientific notation and standard notation.

4.4 I can compute with numbers in scientific notation.

4.5 I can use roots to solve equations with exponents.

New Vocabulary:

• power

• base

• exponent

• scientific notation

• cube root

• perfect cube

Unit 14: Transformation Unit

Calculators allowed: Yes

On the test I will show that...

I can reflect an image on a coordinate plane.

I can translate an image on a coordinate plane.

I can rotate an image on a coordinate plane. 

I can dilate an image on a coordinate plane.

I understand the relationship between the pre-image and the image of a transformation.

I can perform multiple transformations on a figure including a combination of reflections, rotations, translations and dilations.

I can reflect an image on a coordinate plane.

Critical Vocabulary (new):

• transformation

• pre-image

• image

• reflection

• line of reflection

• translation

• rotation

• center of rotation

• clockwise

• counterclockwise

• dilation

• scale factor

• enlargement

• reduction

• composition of transformations

Vocabulary (review):

• horizontal

• vertical

• axis (x and y)

• congruent

• similar