Accelerated Mathematics - 7

District Course #0802

Course Description

Open to: Grade 7 One Year Course
Prerequisite(s): Mathematics 6, survey examination, and counselor approval.
Content: Students will experience a rigorous preparation for algebra with an emphasis on reasoning, problem solving, communication skills, number relationships and theory, patterns and functions, and algebraic concepts.

Adopted Materials

Title: Mathematics: Structure and Method, Course 2
Edition: 1992
Publisher: Houghton Mifflin
ISBN: 0-395-57014-X

Mathematics Curriculum Map
Course overview, activities, vocabulary, supplemental materials in pdf format.

Copyright Resources

Course Scope Semester 1

Course Scope Semester 2

• For specific Standard References please see: Idaho State Assessment Standards
• Download this curriculum and standards documentation as a "Printer Friendly" pdf file

Unit 1

Introduction to Algebra

12 days

0803.01 Use appropriate vocabulary.

Standard Reference
7.M.1.1.8, 7.M.3.4.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use, understand, and apply the appropriate vocabulary given specific mathematical concepts.

Ongoing (Ch. 1-13)

TMA, EOC

0803.02 Understand and use a variety of problem-solving skills.

Standard Reference
7.M.1.1.6

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use a variety of strategies to compute problems drawn from real-world situations.

Ongoing (Ch. 1-13)

TMA, EOC

02

Recognize pertinent information for problem solving.

Ongoing (Ch. 1-13)

TMA, EOC

0803.03 Apply appropriate technology and models to find solutions to problems.

Standard Reference
7.M.1.3.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use computer applications to display and manipulate data.

Ongoing (Ch. 1-13)

TMA, EOC

02

Select appropriate models to represent mathematical ideas.

Ongoing (Ch. 1-13)

TMA, EOC

03

Use calculator to display, manipulate, and compute data.

Ongoing (Ch. 6.6-13)

TMA, EOC

0803.04 Simplify and evaluate algebraic expressions.

Standard Reference
7.M.3.1.2, 7.M.3.2.1, 7.M.3.2.2, 7.M.3.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Simplify or evaluate a mathematical or variable expression using the order of operations.

1-1, 1-2, 1-6, 2-5

TMA, EOC

02

Find the solution of an equation or inequality in one variable whose replacement set is given.

1-3, 1-4

TMA, EOC

03

Write expressions for word phrases, and equations and inequalities for word sentences.

1-6, 1-7

TMA, EOC

04

Simplify the expressions in an equation to obtain an equivalent equation.

5-2

TMA, EOC

Back to Top

Unit 2

The Decimal System

12 days

0803.05 Understand and use exponents.

Standard Reference
7.M.1.1.4, 7.M.1.2.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Read, write, and simplify exponential expressions.

2-2

TMA, EOC

02

Simplify expressions involving negative exponents.

3-7

TMA, EOC

0803.06 Read, write, order, and compare real numbers (integers, fractions, decimals, percents, ratios) and absolute values.

Standard Reference
7.M.1.1.1, 7.M.1.1.2, 7.M.1.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Read, write, and order decimal numbers.

2-2

TMA, EOC

02

Express percents as fractions and as decimals.

7-4

TMA, EOC

03

Express fractions and decimals as percents.

7-4

TMA, EOC

0803.07 Recognize when estimation is appropriate and understand the usefulness of an estimate as distinct from an exact answer.

Standard Reference
7.M.1.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Round decimal numbers and use rounding to estimate an answer.

2-3

TMA, EOC

0803.08 Develop and apply number theory concepts.

Standard Reference
7.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use the properties of addition and multiplication.

2-4

TMA, EOC

02

Use terms and properties concerning positive and negative fractions.

4-1

TMA, EOC

03

Use the addition and multiplication properties of equality.

5-1

TMA, EOC

Back to Top

Unit 3

Positive & Negitive Numbers

13 days

0803.09 Understand the position of real numbers on a number line.

Standard Reference
7.M.1.1.1, 7.M.1.1.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Represent and compare positive and negative integers on a number line.

3-1

TMA, EOC

02

Represent and compare positive and negative decimals on a number line.

3-2

TMA, EOC

0803.10 Consistently and accurately add, subtract, multiply, and divide rational numbers.

Standard Reference
7.M.1.1.5, 7.M.1.2.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the sum of two or more positive or negative numbers.

3-3

TMA, EOC

02

Find the difference of two positive or negative numbers.

3-4

TMA, EOC

03

Find the product of two or more positive or negative numbers.

3-5

TMA, EOC

04

Find the quotient of two positive or negative numbers.

3-6

TMA, EOC

05

Add and subtract fractions and mixed numbers.

4-4

TMA, EOC

06

Multiply fractions and mixed numbers.

4-5

TMA, EOC

07

Divide fractions and mixed numbers.

4-6

TMA, EOC

Back to Top

Unit 4

Rational Numbers

12 days

0803.11 Understand and use real numbers both rational and irrational.

Standard Reference
7.M.1.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Write proper and improper fractions as equivalent fractions or mixed numbers in lowest terms.

4-2

TMA, EOC

02

Write two or more fractions as equivalent fractions with the least common denominator.

4-3

TMA, EOC

03

Write fractions and mixed numbers as equivalent terminating or repeating decimals.

4-7

TMA, EOC

04

Write terminating or repeating decimals as equivalent fractions or mixed numbers.

4-7

TMA, EOC

05

Estimate the positive square root of a positive number by determining the two consecutive integers between which the square root lies.

10-1

TMA, EOC

Back to Top

Unit 5

Equations and Inequalities

14 days

0803.12 Solve one- and two-step equations and inequalities using inverse operations.

Standard Reference
7.M.3.3.1, 7.M.3.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve equations and inequalities by using inverse operations.

1-5

TMA, EOC

02

Solve an equation in one variable that involves addition or subtraction.

5-3

TMA, EOC

03

Solve an equation in one variable that involves multiplication or division.

5-4

TMA, EOC

04

Use several transformations to solve an equation in one variable.

5-5

TMA, EOC

05

Solve an inequality in one variable that involves addition, subtraction, multiplication, or division.

5-6

TMA, EOC

06

Use several transformations to solve an inequality in one variable.

5-7

TMA, EOC

07

Use an equation to solve a word problem.

5-9

TMA, EOC

08

Solve equations involving a percent of increase or decrease.

7-6

TMA, EOC

09

Solve percentage equations involving commissions, royalties, and discounts.

7-7

TMA, EOC

10

Solve equations involving simple and compound interest.

7-8

TMA, EOC

11

Find solutions for an equation in two variables.

8-2

TMA, EOC

0803.13 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models to communicate mathematical information.

Standard Reference
7.M.3.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Intepret an equation as a word problem.

5-8

TMA, EOC

Back to Top

Unit 6

Geometry

16 days

0803.14 Describe, classify, and apply fundamental concepts, properties, and relationships among points, lines, planes, angles, and shapes.

Standard Reference
7.M.4.1.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Name points, segments, rays, lines, and planes.

6-1

TMA, EOC

02

Identify types of angles.

6-3

TMA, EOC

03

Recognize and use the properties of perpendicular lines, complementary angles, supplementary angles, and vertical angles.

6-4

TMA, EOC

04

Identify special angles associated with parallel lines.

6-5

TMA, EOC

05

Classify triangles.

6-6

TMA, EOC

06

Identify quadrilaterals, parallelograms, rhombuses, rectangles, squares, trapezoids, and isosceles trapezoids.

6-7

TMA, EOC

07

Identify and find the perimeters of polygons.

6-8

TMA, EOC

0803.15 Construct and measure various angles and shapes using appropriate tools.

Standard Reference
7.M.4.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Construct and measure segments and angles.

6-1, 6-3

TMA, EOC

02

Determine measures of angles in triangles

6-6

TMA, EOC

03

Construct a parallelogram.

6-7

TMA, EOC

0803.16 Apply formulas for perimeter, circumference, and area to polygons and circles.

Standard Reference
7.M.2.1.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use a circumference formula.

6-2

TMA, EOC

0803.17 Recognize and apply congruence, similarities, and symmetry of shapes.

Standard Reference
7.M.4.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify congruent polygons and their corresponding parts.

6-9

TMA, EOC

02

Apply facts about similar triangles.

10-5

TMA, EOC

Back to Top

Unit 7

Ratio, Proportion & Percent

16 days

0803.18 Understand and use proportions, ratios, and scales.

Standard Reference
7.M.2.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Write a ratio in lowest terms.

7-1

TMA, EOC

02

Set up and solve proportions.

7-1

TMA, EOC

03

Interpret and use scale drawings.

7-3

TMA, EOC

04

Use ratios to solve percentage problems.

7-5

TMA, EOC

05

Use proportions to solve problems involving percents.

7-8

TMA, EOC

0803.19 Use rates to make indirect measurements.

Standard Reference
7.M.2.2.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Express unit rates.

7-2

TMA, EOC

02

Use rates to solve problems.

7-2

TMA, EOC

0803.20 Translate simple word statements and story problems into algebraic expressions and equations.

Standard Reference
7.M.3.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Translate percentage problems into algebraic equations.

7-5

TMA, EOC

Back to Top

Unit 8

The Coordinate Plane

13 days

0803.21 Use the coordinate plane as it relates to real-world applications.

Standard Reference
7.M.4.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Assign coordinates to a point in the plane.

8-1

TMA, EOC

02

Graph and ordered pair of numbers in the coordinate plane.

8-1

TMA, EOC

03

Graph a linear equation in two variables.

8-3

TMA, EOC

05

Solve problems using graphs.

8-5

TMA, EOC

Back to Top

Unit 9

Areas & Volumes

14 days

0803.22 Apply formulas for perimeter, circumference, and area to polygons and circles.

Standard Reference
7.M.2.1.6, 7.M.2.1.4, 7.M.4.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the areas of rectangles and triangles.

9-1

TMA, EOC

02

Find the areas or parallelograms and trapezoids.

9-2

TMA, EOC

03

Find the areas of circles and of regions involving circles.

9-3

TMA, EOC

04

Use point and line symmetry in finding the areas of figures.

9-4

TMA, EOC

0803.22 Understand the concept of surface area and volume (capacity).

Standard Reference
7.M.4.1.6

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the volumes and capacities of prisms, cylinders, pyramids, and cones.

9-5, 9-6

TMA, EOC

02

Find the surface areas of prisms and cylinders.

9-7

TMA, EOC

Back to Top

Unit 10

Square Roots & Right Triangles

7 days

0803.24 Investigate right triangle geometry using the Pythagorean Theorem.

Standard Reference
7.M.4.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use the Pythagorean Theorem and its converse.

10-4

TMA, EOC

Back to Top

Unit 11

Probability

7 days

0803.25 Understand and use the language of probability.

Standard Reference
7.M.5.4.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the number of permutations or combinations that can be made from a group of objects.

11-1, 11-2

TMA, EOC

02

Determine the odds in favor of an event and the odds against an event.

11-4

TMA, EOC

0803.26 Recognize equally likely outcomes.

Standard Reference
7.M.5.4.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the probability of an event when the outcomes are equally likely.

11-3

TMA, EOC

Back to Top

Unit 12

Statistics

6 days

0803.27 Analyze and interpret tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).

Standard Reference
7.M.5.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Read single and double bar graphs.

12-1

TMA, EOC

02

Read line graphs.

12-2

TMA, EOC

03

Read frequency distribution tables.

12-4

TMA, EOC

04

Read stem-and-leaf plots.

12-5

TMA, EOC

0803.28 Collect, organize, and display data with appropriate notation in tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).

Standard Reference
7.M.5.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Make single and double bar graphs.

12-1

TMA, EOC

02

Make line graphs.

12-2

TMA, EOC

03

Make frequency distribution tables.

12-4

TMA, EOC

04

Make stem-and-leaf plots

12-5

TMA, EOC

0803.29 Choose and calculate the appropriate measure of central tendency – mean, median, and mode.

Standard Reference
7.M.5.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Calculate the mean, median, and mode of a set of data.

12-3

TMA, EOC

0803.30 Explore the significance of range, frequency, and informal distribution.

Standard Reference
7.M.5.3.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Calculate the range of a set of data.

12-3

TMA, EOC

Back to Top

Unit 13

Polynomials

6 days

0803.31 Explore the concept of polynomials and the basic techniques by which polynomials are manipulated.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Introduce polynomials and the terminology associated with them.

13-1

TMA, EOC

02

Add and subtract polynomials.

13-2

TMA, EOC

03

Multiply and divide polynomials.

13-3

TMA, EOC

04

Multiply and divide a polynomial by a monomial.

13-4

TMA, EOC