Highlights of the New Learning for Grade-Six Students Are

Grade 6

Overview

This overview provides only the highlights of the new learning that should take place at the sixth-grade level. The specific skills and subject matter that sixth graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators:

16An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding.

17An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency.

18An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-six students are

understanding the concepts of percentages and integers,
comparing rational numbers and percentages,
applying an algorithm to add and subtract fractions,
generating strategies to multiply and divide fractions and decimals,
understanding the concepts of exponents and powers of ten,
applying order of operations,
using inverse operations to solve one-step equations,
representing location of points in all four quadrants,
constructing two-dimensional shapes with rotational symmetry,
classifying shapes as similar,
identifying pairs of angles that are complementary or supplementary,
applying strategies and formulas to approximate circumference and area of a circle,
applying strategies and procedures to estimate and determine perimeters and areas of irregular shapes,
using proportions to determine unit rates,
using a scale to determine distance, and
applying procedures to calculate the probability ofcomplementary events.

Grade 6

Mathematical Processes

The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes.

Standard 6-1:The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

The indicators for this standard, which are appropriate for grades six though eight, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students.

Indicators

6-1.1Generate and solve complex abstract problems that involve modeling physical, social, and/or mathematical phenomena.

6-1.2Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

6-1.3Use inductive and deductive reasoning to formulate mathematical arguments.

6-1.4Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

6-1.5Generalize mathematical statements based on inductive and deductive reasoning.

6-1.6Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks.

6-1.7Generalize connections among a variety of representational forms and real-world situations.

6-1.8Use standard and nonstandard representations to convey and support mathematical relationships.

Unitedstreaming.com Grades 6 - 8

Search – math problem solving –14 lessons

math reasoning—3 lessons

math proofs—1 lesson

math communications—6 lessons

math connections—1 lesson

math representation—7 lessons

Grade 6

Number and Operations

Standard 6-2:The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

Indicators /

Lesson Plans

Diagnostic Tests /

Challenge the PACT Workbook Pages 1 – 11
Buckle Down PACT Form A

6-2.1Understand whole-number percentages through 100. /

Fantastic Five
Buckle Down PACT Pages 49 – 51
PACT Workbook Pages 5 – 6

6-2.2Understand integers. /

Fantastic Five
Buckle Down PACT Pages 9 – 10
PACT Workbook Pages 13 – 14
Challenge the PACT Workbook Pages 112 – 123
Glencoe Lesson 11-1
Lesson 11-1 Power Point
Subtracting Integers Power Point
Integers Power Point
Integers Power Point
Integers Power Point
Adding and Subtracting Integers Review Power Point
Integers Review Power Point
Integers Study Guide
Integers Test
Unitedstreaming.com Grade 6-8 (Page 1 – 9 lessons)

6-2.3Compare rational numbers and whole-number percentages through 100 by using the symbols ≤, ≥, <, >, and =. /

Fantastic Five
Buckle Down PACT Pages 30 – 32
Buckle Down PACT Pages 41 – 42
PACT Workbook Pages 3 – 4
Challenge the PACT Workbook Page 39
Challenge the PACT Workbook Pages 116 – 117
Glencoe Lesson 3-3
Glencoe Lesson 5-8
Glencoe Lesson 11-2
Lesson 3-3 Power Point
Lesson 5-8 Power Point
Lesson 11-2 Power Point
Unitedstreaming.com Grade 6-8 Search – inequalities (6 lessons)

6-2.4Apply an algorithm to add and subtract fractions. /

Fantastic Five
Buckle Down PACT Pages 33 – 34
Challenge the PACT Workbook Pages 57 – 67
Glencoe Lesson 6-3
Glencoe Lesson 6-4
Glencoe Lesson 6-5
Glencoe Lesson 6-6
Lesson 6-4 Power Point
Lesson 6-5 Power Point
Lesson 6-6 Power Point
Simplifying Fractions Power Point
Mixed Numbers Power Point
Improper Fractions Power Point
Unitedstreaming.com Grade 6 - IIIA1(2 lessons)

6-2.5Generate strategies to multiply and divide fractions and decimals. /

Fantastic Five
Buckle Down PACT Pages 35 – 40
Buckle Down PACT 45 – 48
Challenge the PACT Workbook Pages 42 – 44
Challenge the PACT Workbook Pages 68 – 72
Glencoe Lesson 4-1
Glencoe Lesson 4-3
Glencoe Lesson 4-5
Glencoe Lesson 4-6
Glencoe Lesson 4-7
Glencoe Lesson 7-2
Glencoe Lesson 7-3
Glencoe Lesson 7-5
Glencoe Lesson 7-6
Lesson 4-1 Power Point
Lesson 4-3 Power Point
Lesson 4-5 Power Point
Lesson 4-6 Power Point
Lesson 4-7 Power Point
Lesson 7-2 Power Point
Lesson 7-3 Power Point
Lesson 7-5 Power Point
Lesson 7-6 Power Point
Unitedstreaming.com Grade 6-8 Search – * & / fractions (3 lessons)

6-2.6Understand the relationship between ratio/rate and multiplication/division. /

Fantastic Five
PACT Workbook Pages 7 – 8
Challenge the PACT Workbook Pages 52 – 56
Glencoe Lesson 8-1
Lesson 8-1 Power Point
Ratio Power Point
Unitedstreaming.com Grade 6-8 Search – ratios :Page 1 (4 lessons)

6-2.7Apply strategies and procedures to determine values of powers of 10, up to 106. /

Fantastic Five
Buckle Down PACT Pages 18 – 19
PACT Workbook Pages 9 – 10
Exponents (Powers of Ten) Power Point
Unitedstreaming.com Grade 6-8 Search – exponents (First 7 lessons)

6-2.8Represent the prime factorization of
numbers by using exponents. /

Fantastic Five
Buckle Down PACT Pages 20 – 23
Challenge the PACT Workbook Pages 152 – 154
Glencoe Lesson 5-2
Lesson 5-2 Power Point
Prime Factor Tree Power Point
Divisibility Rules Power Point
Exponents Power Point
Prime and Composite Numbers Power Point
Unitedstreaming.com Grade 6-8 Search – prime factorization (2 lessons)

6-2.9Represent whole numbers in exponential form. /

Fantastic Five
Glencoe Lesson 1-6

Additional Number and Operations Indicators /

Fantastic Five
Challenge the PACT Workbook Pages 48 – 51
PACT Workbook Pages 1 – 2, 11 – 12,
15 – 16, 19 – 20, 25 – 26, 27 – 28

Grade 6

Algebra

Standard 6-3:The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

Indicators / Lesson Plans
6-3.1Analyze numeric and algebraic patterns and pattern relationships. /

Fantastic Five
Buckle Down PACT Pages 93 – 98
PACT Workbook Pages 29 – 30
Glencoe Lesson 1-2
Glencoe Lesson 7-8
Lesson 7-8 Power Point
Unitedstreaming.com Grade 6 –Search patterns—3 choices

6-3.2Apply order of operations to simplify whole-number expressions. /

Fantastic Five
Buckle Down PACT Pages 24 – 25
PACT Workbook Pages 31 – 32
Challenge the PACT Workbook Pages 98 – 100
Glencoe Lesson 1-4
Unitedstreaming.com Grade 6 – Search order of operations—1 choice

6-3.3Represent algebraic relationships with variables in expressions, simple equations, and simple inequalities. /

Fantastic Five
Buckle Down PACT Pages 82 – 85
Glencoe Lesson 1-5
Unitedstreaming.com Grade 6 – Search equations—1 choice

6-3.4Use the commutative, associative, and distributive properties to show that two expressions are equivalent. /

Fantastic Five
Buckle Down PACT Pages 78 – 81
Glencoe Lesson 4-2
PACT Workbook Pages 17 – 18
PACT Workbook Pages 35 – 36
Challenge the PACT Workbook Pages 107 – 111
Lesson 4-2 Power Point
Properties Power Point
Properties Power Point
Properties Review Power Point
Properties Study Guide
Properties Practice Test
Properties Test
Unitedstreaming.com Grade 6 – Search order of operations—1 choice

6-3.5Use inverse operations to solve one-step equations that have whole-number solutions and variables with whole-number coefficients. /

Fantastic Five
Glencoe Lesson 12-1
Glencoe Lesson 12-2
Glencoe Lesson 12-3
Lesson 12-1 Power Point
Lesson 12-2 Power Point
Lesson 12-3 Power Point
Unitedstreaming.com Grade 6 – Search equations—1 choice

Additional Algebra Indicators /

Fantastic Five
Challenge the PACT Workbook Pages 124 – 130, 131, 132 – 139
PACT Workbook Pages 33 – 34, 37 – 38

Grade 6

Geometry

Standard 6-4:The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

Indicators / Lesson Plans
6-4.1Represent with ordered pairs of integers the location of points in a coordinate grid. /

Fantastic Five
Challenge the PACT Workbook Pages 247 – 256
Glencoe Lesson 2-9
Glencoe Lesson 11-7
Lesson 2-9 Power Point
Lesson 11-7 Power Point
Battlegraph Power Point

6-4.2Apply strategies and procedures to find the coordinates of the missing vertex of a square, rectangle, or right triangle when given the coordinates of the polygon’s other vertices. /

Fantastic Five
Buckle Down PACT Pages 126 – 128
PACT Workbook Pages 47 – 48

6-4.3Generalize the relationship between line symmetry and rotational symmetry for two-dimensional shapes. /

Fantastic Five
Buckle Down PACT Pages 120 – 122
Symmetry Power Point

6-4.4Construct two-dimensional shapes
with line or rotational symmetry. /

Fantastic Five
PACT Workbook Pages 43 – 44

6-4.5Identify the transformation(s) used to move a polygon from one location to another in the coordinate plane. /

Fantastic Five
Buckle Down PACT Pages 117 – 119

6-4.6Explain how transformations affect the location of the original polygon in the coordinate plane. /

Fantastic Five
Buckle Down PACT Pages 129 – 133
PACT Workbook Pages 51 – 52

6-4.7Compare the angles, side lengths, and perimeters of similar shapes. /

Fantastic Five
Buckle Down PACT Pages 113 – 114
PACT Workbook Pages 41 – 42

6-4.8Classify shapes as similar. /

Fantastic Five
Buckle Down PACT Pages 111 – 112
PACT Workbook Pages 45 – 46
Glencoe Lesson 9-6
Lesson 9-6 Power Point

6-4.9Classify pairs of angles as either complementary or supplementary. /

Fantastic Five
Glencoe Lesson 9-1
Lesson 9-1 Power Point

Additional Geometry Indicators /

Fantastic Five
Challenge the PACT Workbook Pages 172 – 174
PACT Pages 39 – 40, 49 – 50, 53 – 54, 55 – 56, 57 – 58, 59 – 60

Grade 6

Measurement

Standard 6-5:The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

Indicators / Lesson Plans
6-5.1Explain the relationships among the circumference, diameter, and radius of a circle. /

Fantastic Five
Glencoe Lesson 7-4
Unitedstreaming.com Grade 6 – Search circumference—1 choice

6-5.2Apply strategies and formulas with an approximation of pi (3.14, or ) to find the circumference and area of a circle. /

Fantastic Five
Challenge the PACT Workbook Pages 235 – 240
Glencoe Lesson 7-4
Glencoe Lesson 10-3
Lesson 10-3 Power Point
Circle Study Guide
Circle Test

6-5.3Generate strategies to determine the surface area of a rectangular prism and a cylinder. /

Fantastic Five
Challenge the PACT Workbook Pages 212 – 219
Glencoe Lesson 10-6
Lesson 10-6 Power Point

6-5.4 Apply strategies and procedures to
estimate the perimeters and areas of
irregular shapes. /

Fantastic Five
PACT Workbook Pages 67 - 68

6-5.5Applystrategies and procedures of
combining and subdividing to find the perimeters and areas of irregular shapes. /

Fantastic Five
Buckle Down PACT Pages 163 – 165
Buckle Down PACT Pages 169 – 171

6-5.6Use proportions to determine unit
rates. /

Fantastic Five

6-5.7Use a scale to determine distance. /

Fantastic Five
Buckle Down PACT Pages 152 – 153

6-5.7 Use a scale to determine distance. /

Fantastic Five
PACT Workbook Pages 75 - 76
Challenge the PACT Workbook Pages 196 – 198
Glencoe Lesson 8-3
Lesson 8-3 Power Point

Additional Measurement Indicators /

Fantastic Five
PACT Workbook Pages 61 - 62, 62 – 63, 65 – 66, 69 – 70, 71 – 72, 73 - 74

Grade 6

Data Analysis and Probability

Standard 6-6:The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

Indicators / Lesson Plans
6-6.1Predict the characteristics of one
population based on the analysis of sample data. /

Fantastic Five
Navigating through Data Analysis Chapter 4
Navigating through Probability Chapter 3
Unitedstreaming.com Grade 6 – IVB2 Page 10 of 10 (1 lesson)

6-6.2Organize data in frequency tables, histograms, or stem-and-leaf plots as appropriate. /

Fantastic Five
Navigating through Data Analysis Chapters 1 and 2
Buckle Down PACT Pages 193 – 196
Glencoe Lesson 2-1
Glencoe Lesson 2-2
Glencoe Lesson 2-6
Lesson 2-2 Power Point
Unitedstreaming.com Grade 6 – IB1 Page 9 of 10 (5 lessons)

6-6.3Analyze which measure of central tendency (mean, median, or mode) is the most appropriate for a given purpose. /

Fantastic Five
Navigating through Data Analysis Chapter 2
Buckle Down PACT Pages 185 – 190
Challenge the PACT Workbook Pages257 – 268
Glencoe Lesson 2-7 (teacher integrate own questions)
Lesson 2-7 Power Point
Mean, Median, Mode Power Point
Unitedstreaming.com Grade 6 – IIA1 Page 9 of 10 (2 lessons)

6-6.4Use theoretical probability to determine the sample space and probability for one- and two-stage events such as tree diagrams, models, lists, charts, and pictures. /

Fantastic Five
Navigating through Probability Chapters 1, 2, 3, and 4
Buckle Down PACT Pages 199 – 201
Buckle Down PACT Pages 204 – 207
Challenge the PACT Workbook Pages 269 - 277
Glencoe Lesson 13-1
Glencoe Lesson 13-4
Lesson 13-1 Power Point
Lesson 13-4 Power Point
Unitedstreaming.com Grade 6 – IIIB Page 9 of 10 (2 lessons)
Unitedstreaming.com Grade 6 – IVB1 Page 10 of 10 (1 lesson)

6-6.5Apply procedures to calculate the probability of complementary events. /

Fantastic Five
Navigating through Probability Chapter 4
Buckle Down PACT Pages 202 - 203

Unitedstreaming.com Grade 6 –

Data Analysis and Probability Standard 6-6

Search statistics and data analysis—1 choice

BrainPop

6-2.8

6-3.2

6-3.3

6-3.5

6-4.1

6-4.4 & 6-4.5

6-5.2

6-6.4

Grade 7

Overview

This overview provides only the highlights of the new learning that should take place at the seventh-grade level. The specific skills and subject matter that seventh graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators:

19An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding.

20An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency.

21An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-seven students are

understanding fractional percentages and percentages greater than 100;
understanding the concept of square roots and the inverse relationship between squaring and finding square roots of perfect squares;
understanding the meaning of absolute value;
generating strategies to add, subtract, multiply, and divide integers;
applying an algorithm to multiply and divide fractions and decimals;
using inverse operations to solve two-step equations and inequalities;
classifying and explaining proportional relationships;
translating between two- and three-dimensional representations of compound figures;
creating tessellations with transformations and explaining the angle-measure relationships among shapes that tessellate;
applying strategies and formulas to determine the surface area and volume of three-dimensional shapes;
using one-step unit analysis to convert between and within U.S. Customary System and the metric system; and
applying procedures to calculate the interquartile range and the probability of mutually exclusive events.

Grade 7

Mathematical Processes

The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes.

Standard 7-1:The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators

7-1.1Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena.

7-1.2Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

7-1.3Use inductive and deductive reasoning to formulate mathematical arguments.

7-1.4Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

7-1.5Generalize mathematical statements based on inductive and deductive reasoning.