Mathematics - Sixth Grade

Course Description

The elementary mathematics curriculum of the Boise School District is vibrant, -challenging, and child-centered. With consideration for children's needs and their development, the following NCTM strands, which are of equal importance, will comprise the elementary mathematics curriculum: (1) Numbers and Numeration, (2) Organizing and Interpreting Data, (3) Problem Solving, (4) Measurement, (5) Geometry, (6) Technology, and (7) Algebra – the language of mathematics. However, instruction will be structured as a spiral of strands to insure that children will experience mathematics as a unified whole rather than as a set of disjointed, unrelated parts. In particular, problem solving and technology should integrate the curriculum across strand and among other disciplines.

Meaning and understanding of mathematics rests upon the foundation of mathematical concepts developed through frequent experience with concrete manipulatives. It is recommended that manipulatives be used as often as possible. Concepts and skills should not be taught in isolation. Both are built on students’ past knowledge through meaningful examples and experiences, and students should be provided ample opportunities to apply them to practical, real-life situations.

Adopted Materials

Title: Houghton Mifflin Math
Edition: 2005
Publisher: Houghton Mifflin Company
ISBN: 0-618-33869-1

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

Copyright Resources

Course Scope

(view Mathematics Curriculum Map for Sequence)

• For specific Standard References please see: Idaho State Assessment Standards
• Download this curriculum and standards documentation as a "Printer Friendly" pdf file
• Curriculum updated: 08/14/2007

Unit 1

Understand and use numbers

4-5 weeks

608.01 Read, write, order and compare whole numbers, fractions and decimals.

Standard Reference
6.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify the largest or smallest number in a given set of whole numbers.

Ch. 1

TMA

02

Identify the largest or smallest number in a given set of decimal numbers.

Ch. 1,4

TMA

03

Identify or write a set of positive whole numbers and decimals arranged in order from greatest to least or least to greatest.

Ch. 1,4

TMA

608.02 Show a sense of magnitudes and relative magnitudes of real numbers (whole numbers, fractions and decimals).

Standard Reference
6.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Place positive and negative whole numbers and decimals on a number line.

Ch. 1,11

TMA

608.03 Explore the use of integers in real world situations.

Standard Reference
6.M.1.1.7

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Explore the use of integers in real world situations.

Ch. 11

TO

608.04 Use appropriate vocabulary

Standard Reference
6.M.1.1.8

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate vocabulary.

Dist. List

TO

Back to Top

Unit 2

Perform computations accurately

4-5 weeks

608.05 Consistently and accurately multiply and divide whole numbers.

Standard Reference
6.M.1.2.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the product or quotient of whole numbers (up to four digit factors, or three digit divisors with six digit dividends).

Ch. 2

TMA

608.06 Add, subtract, multiply and divide decimals.

Standard Reference
6.M.1.2.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the sum or difference of three or four place decimal numbers.

Ch. 1,7

TMA

02

Find the product or quotient consisting of three or four decimal places.

Ch. 7

TMA

608.07 Instantly recall basic multiplication and division facts from a 12 x 12 times table.

Standard Reference
6.M.1.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Instantly recall basic multiplication and division facts from a 12 x 12 times table.

12 x 12 Multiplication Tables, MAD Minutes

TMA

608.08 Evaluate numerical expressions using the order of operations.

Standard Reference
6.M.1.2.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Simplify numerical expressions using the order of operations.

Ch. 2

TMA

608.09 Select and use an appropriate method of computation from mental math, paper and pencil, calculator or a combination of the three.

Standard Reference
6.M.1.2.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Select and use an appropriate method of computation from mental math, paper and pencil, calculator or a combination of the three.

Text

TO

608.10 Use appropriate vocabulary.

Standard Reference
6.M.1.2.6

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate mathematical vocabulary.

District List

TO

Back to Top

Unit 3

Estimate and judge reasonableness of results

Ongoing

608.11 Use estimation to predict computation results.

Standard Reference
6.M.1.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the reasonableness of solutions to computation and word problems, choosing an appropriate method (e.g., using estimation, evaluating according to context).

Text

TO

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

Standard Reference
6.M.1.3.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine whether a given problem situation calls for an estimated or an exact answer.

Text

TO

608.13 Determine whether a given estimate is an overestimate or underestimate.

Standard Reference
6.M.1.3.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine whether a given estimate is an overestimate or underestimate.

Ch. 2,Text

TO

608.14 Use a four-function calculator to solve complex grade-level problems

Standard Reference
6.M.1.3.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use a four-function calculator to solve complex grade-level problems

Resource Ref.

TO

608.15 Use appropriate vocabulary.

Standard Reference
6.M.1.3.6

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate mathematical vocabulary.

District List

TO

Back to Top

Unit 4

Understand and use a variety of problem-solving skills

Ongoing

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

Standard Reference
6.M.1.2.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use calculators, computers and other tools to solve mathematical problems.

Text

TO

608.17 Solve problems using the four-step process of problem solving (explore, plan, solve, examine).

Standard Reference
6.M.1.1.6

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve problems using the four-step process of problem solving: explore (understand), plan, solve, examine(look back).

Student Handbook XXVI, Text

TO

608.18 Make predictions and decisions based on information.

Standard Reference
6.M.5.5.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Make predictions and decisions based on information.

Text

TO

Back to Top

Unit 5

Use reasoning skills to recognize problems and express them mathematically

Ongoing

608.19 Use a variety of methods such as words, numbers, symbols, charts, graphs, tables, diagrams and models to explain mathematical reasoning and concepts.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Describe or explain a problem situation or a mathematical concept orally or in writing.

Ch.1, 9-10,Text

TO

02

Create or identify an appropriate oral, written, concrete, pictorial, graphic and/or algebraic model for a problem situation.

Text,The Problem Solver

TO

608.20 Apply solutions and strategies to new problem situations.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Apply the solutions or strategies from a problem to similar problems or to new context.

Text

TMA

608.21 Formulate conjectures and discuss why they must be or seem to be true.

Standard Reference
6.M.1.3.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use logic to make a conjecture or draw a conclusion about a situation.

Text

TO

Back to Top

Unit 6

Apply appropriate technology and models to find solutions to problems

Ongoing

608.22 Understand the purpose and capabilities of appropriate technology use as a tool to solve problems.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use calculators, computers and other tools to solve mathematical problems.

Text, TI calculators, www.eduplace.com

TO

608.23 Use computer applications to display and manipulate data.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use computer applications to display and manipulate data.

MS Excel and MS Access, Internet

TO

608.24 Select appropriate models to represent mathematical ideas.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Select appropriate models to represent mathematical ideas

Text

TO

Back to Top

Unit 7

Communicate results using appropriate terminology and methods

Ongoing

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

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

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

Text

TO

608.26 Use appropriate vocabulary to communicate mathematical information.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate vocabulary to communicate mathematical information.

District vocabulary list

TO

608.27 Use appropriate notation.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate notation to communicate mathematical information.

Text

TO

Back to Top

Unit 8

Use algebraic symbolism as a tool to represent mathematical relationships

Ongoing

608.28 Explore the meaning and use of variables of simple expressions and equations.

Standard Reference
6.M.3.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Substitute a given number for a variable in simple algebraic expressions and equations.

Ch 1, 11

TMA

608.29 Translate simple word statements and story problems into algebraic equations.

Standard Reference
6.M.3.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Translate an English phrase or sentence into an algebraic expression or equation.

Ch 1

TMA

608.30 Use symbols (>, <, =) to express relationships.

Standard Reference
6.M.3.1.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use symbols (>, <, =) to express relationships.

Ch.1,4,11,17

TMA

Back to Top

Unit 9

Evaluate algebraic expressions

Ongoing

608.31 Explore and use the following properties in evaluating mathematical and algebraic expressions: commutative, associative, identity, zero, inverse, and distributive.

Standard Reference
6.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use the commutative, associative, identity, zero, inverse, and distributive properties to evaluate expressions.

Ch. 1-2

TMA

608.32 Explore the order of operations.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use the order of operations to evaluate expressions.

Ch. 2

TMA

Back to Top

Unit 10

Solve algebraic equations and inequalities

Ongoing

608.33 Evaluate simple algebraic expressions using substitutions

Standard Reference
6.M.1.1.7

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate simple algebraic expressions using substitution

Text
Hands on Equations

TO

608.34 Solve one-step equations using inverse operations with whole numbers.

Standard Reference
6.M.3.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Write and/or solve one-variable addition, subtraction, multiplication, and/or division equations.

Text
Hands on Equations

TMA

Back to Top

Unit 11

Understand data analysis

1 week

608.35 Read and interpret tables, charts, and graphs (line graphs, bar graphs, frequency lines or line plots, and circle graphs).

Standard Reference
6.M.5.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Interpret data given in a list, table, or symbolic graph.

Ch. 9,10,13

TMA

608.36 Explain and justify conclusions drawn from tables, charts, and graphs.

Standard Reference
6.M.5.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Explain and justify conclusions drawn from tables, charts, and graphs.

Ch. 9,10,13

TO, TMA

608.37 Use appropriate vocabulary.

Standard Reference
6.M.5.1.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate mathematical vocabulary.

District List

TO

Back to Top

Unit 12

Collect, organize, and display data

Ongoing

608.38 Collect, organize, and display data with appropriate notation in tables, charts, and graphs (line graphs, bar graphs, frequency lines or line plots, and circle graphs).

Standard Reference
6.M.5.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Create or identify graphic representations of given or collected data.

Ch. 9,10

TMA

Back to Top

Unit 13

Apply simple statistical measurements

1 week

608.39 Find measures of central tendency – mean, median, and mode – with simple sets of data.

Standard Reference
6.M.5.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Compute the mean, median, or mode for information presented in a table, graph, or data set.

Ch. 9,10

TMA

608.40 Determine the range of a set of data.

Standard Reference
6.M.5.3.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the range of a set of data.

Ch. 9,10

TMA

Back to Top

Unit 14

Understand the concept of functions

1 week

608.41 Extend patterns and identify a rule (function) that generates the pattern using whole numbers, decimals, and fractions.

Standard Reference
6.M.3.4.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify the function rule that represents the relationship in a series of related numbers.

Ch. 1,13

TMA

608.42 Discover, describe, and extend patterns by using manipulatives and pictorial representations.

Standard Reference
6.M.3.4.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Discover, describe, and extend patterns by using manipulatives and pictorial representations.

Text

TMA

608.43 Use appropriate vocabulary.

Standard Reference
6.M.3.4.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate mathematical vocabulary.

District List

TO

608.44 Use mathematical models to show change in real context.

Standard Reference
6.M.3.4.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use mathematical models to show change in real context.

Ch. 9,10,11,13

TMA

Back to Top

Unit 15

Apply functions to a variety of problems

1 week

608.45 Use patterns and functions to represent and solve simple problems.

Standard Reference
6.M.3.6.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use patterns and functions to represent and solve simple problems.

Ch. 1,2,13

TMA

Back to Top

Unit 16

Understand and use numbers

2-3 weeks

608.46 Read, write, order, and compare whole numbers, fractions, and decimals.

Standard Reference
6.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify the largest or smallest fractions in a given set of fractions.

Ch. 4

TMA

02

Identify or write a set of fractions arranged in order from greatest to least or least to greatest.

Ch. 4

TMA

608.47 Understand the use of fractions and decimals and their interrelationship.

Standard Reference
6.M.1.1.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Convert decimals and fractions interchangeably.

Ch. 4

TMA

608.48 Expand the use of decimals and fractions to explore the use of percents and ratios.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Expand the use of decimals and fractions to explore the use of percents and ratios.

Ch. 4,16,17,18

TMA

608.49 Show a sense of magnitudes and relative magnitudes of real numbers (whole numbers, fractions and decimals).

Standard Reference
6.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Place fractions on a number line.

Ch. 4

TMA

608.50 Develop and apply number theory concepts (prime, composite, greatest common factor, lowest common multiple and prime factorization.)

Standard Reference
6.M.1.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify the greatest common factor of two whole numbers.

Ch. 3

TMA

02

Identify the least common multiple of two whole numbers.

Ch. 3

TMA

03

Identify prime numbers between 1 and 100.

Ch. 3

TMA

04

Identify the prime factors of a numbers.

Ch. 3

TMA

Back to Top

Unit 17

Perform computations accurately

4-5 weeks

608.51 Add and subtract fractions with unlike denominators and simplify as necessary.

Standard Reference
6.M.1.2.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Add and subtract fractions with unlike denominators and simplify as necessary.

Ch. 5

TMA

608.52 Explore the use of exponents.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate numerical expressions using exponents.

Ch. 1,7

TMA

608.53 Explore multiplication and division of fractions.

Standard Reference
6.M.1.2.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the product or quotient of fractions and mixed numbers.

Ch. 6

TMA

Back to Top

Unit 18

Understand basic concepts of probablilty

1 week

608.54 Predict, perform, and record results of simple probability experiments.

Standard Reference
6.M.5.4.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the probability of a particular outcome of a specific event (e.g., choosing an object, spinning a spinner) and represent the probability as a ratio, decimal, proportion, or percent.

Ch. 19

TMA

608.55 Use appropriate vocabulary.

Standard Reference
6.M.5.4.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate mathematical vocabulary.

District List

TO

Back to Top

Unit 19

Make predictions or decisions based on data

1 week

608.56 Make predictions based on simple experimental probabilities.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Predict a probable future event based on a table or graph, or predict the probable outcome of a specific event (e.g., choosing an object, spinning a spinner, tossing a coin).

Ch. 9,10,19

TMA

608.57 Use appropriate vocabulary.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use appropriate mathematical vocabulary.

District List

TO

Back to Top

Unit 20

Apply concepts of rates and other derived or indirect measurements

1 week

608.58 Explore the use of rates to make indirect measurements.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use rates to make calculations.

Ch. 16

TMA

Back to Top

Unit 21

Apply the concepts of ratios and proportions

1 week

608.59 Explore the use of proportions, ratios, and scales.

Standard Reference
6.M.2.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use ratios to solve word problems.

Ch. 16

TMA

02

Use proportions to solve word problems.

Ch. 16

TMA

Back to Top

Unit 22

Apply dimensional analysis

1 week

608.60 Understand units and their relationship to one another and to real-world applications.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Understand units and their relationship to one another and to real-world applications.

Ch. 8

TMA

Back to Top

Unit 23

Apply concepts of size, shape and special relationships

4 weeks

608.61 Precisely describe, classify, and understand relationships among types of one-, two-, and three-dimensional objects using their defining properties.

Standard Reference
6.M.4.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify or describe the attributes of geometric figures, including two- or three-dimensional shapes, line segments, angles, points, arcs, and rays.

Ch. 8,14,15,20

TMA

02

Use the geometric terminology for figures and their parts (e.g., point, line, plane, angle, diameter, radius).

Ch. 8,14,15,20

TMA

03

Use of geometric terminology for relationships (e.g. - parallel, perpendicular, vertical, adjacent, complementary, supplementary).

Ch. 8,14

TMA

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

Standard Reference
6.M.4.1.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use a protractor to determine the measure of an angle.

Ch. 14,15

TMA

02

Find the measure of a missing angle using the properties of complementary and supplementary angles and knowledge of the sum of angles.

Ch. 14,15

TMA

03

Draw or construct geometric figures (right, acute, or obtuse angles; right, scalene, isosceles, and equilateral triangles; and quadrilaterals) using appropriate tools.

Ch. 14,15

TMA

608.63 Apply fundamental concepts, properties, and relationships among points, lines, angles and shapes.

Standard Reference
6.M.4.1.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Apply fundamental concepts, properties, and relationships among points, lines, angles and shapes.

Ch. 8,14,15

TMA

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

Standard Reference
6.M.4.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify lines of symmetry occurring in a geometric figure.

Ch. 15

TMA

02

Identify similar or congruent relationships occurring in geometric