Sixth Grade

**Notice that not all lessons in a Harcourt Chapter are included. These were intentionally removed because they do not address Common Core Standards. You will not need to fill time with activities unrelated to the standards. Instead use this gift of time to help your students develop a deeper conceptual understanding of the mathematical concepts presented in the standards.

Unit One: Number Sense and Operations

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.NS.2 /
  • Algorithm for division of multi-digit numbers
/ 1.4
4.6 /
  • Decimals and fractions as remainders
/
  • HC p. 24B Advanced Learners & Alternative Teaching Strategy (division activities- use fractions or decimals not remainders)

6.EE.5 /
  • Understand solving an equation
/ 2.2 /
  • The focus in this unit is on the equations, inequalities will be addressed in a later unit
/
  • HC p. 38B Special Needs, Alternative Teaching Strategy

6.EE.1 /
  • Write and evaluate numerical expressions involving whole-number exponents
/ 2.5 /
  • HC p. 46B Alternative Teaching Strategy, Writing in Mathematics

6.EE.2
6.EE.3 /
  • Write variable expressions
  • Read and identify expressions using mathematical terms
  • Evaluate variable expressions paying attention to Order of Operations
  • Apply properties of operations to write expressions in multiple ways
/ 2.1
2.6 /
  • 2.3 property background
  • Apply the properties to show expressions in multiple ways throughout 2.1 and 2.6
/
  • HC p. 36B Alternative Teaching Strategy, Early Finishers
  • Algebra Readiness/ Everyday Counts calendar for May/June

6.NS.3 /
  • Algorithm to add, subtract, multiply, and divide multi-digit decimals
/ 4.1
4.2
4.3
4.4
4.5
4.7 /
  • HC p.76B Alternative Teaching Strategy & Early Finishers
  • HC p. 78 Alternative Teaching Strategy
  • HC p. 80B Alternative Teaching Strategy, Advanced Learners
  • HC p. 80 Math Lab
  • HC p. 82 Alternative Teaching Strategy
  • HC p. 84 Writing
  • HC p. 86B Alternative Teaching Strategy, Early Finishers
  • HC p. 88 Math Lab

6.EE.6 /
  • Write variable expressions to solve real-world or mathematical problems
/ 4.7 /
  • Add in a solving component to this lesson
/
  • HC challenge worksheet

Unit Two: Statistics and Graphing

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.SP.1
6.SP.2
6.SP.3
6.SP.4
6.SP.5 /
  • Statistical question
  • Data
  • Measure of center (median, mean, and mode)
  • Number line
  • Dot plots
  • Histograms
  • Box plots (box-and-whisker plot)
  • Survey summaries
-How to report observations and how data was collected
-How to describe mean and median of the data set / 5.6 collect data (explain sample size)
5.3 line plots
6.4 & 6.5 box-and-whisker plots (box plots)
6.3 histograms
5.4 mean, median, and mode
p. 155 Scatterplots (dot plots) /
  • Be sure to complete surveys and discuss the emphasized attributes with your class. You can find ideas in the Harcourt lessons listed. Do not teach the whole lessons.
  • Please get information from your local newpaper to explore statistics in a fun, interactive way.
  • After completing a survey, make all four types of graphs to display data then have students determine the best graph.
  • You are responsible for teaching an IEFA lesson for this standard. An example lesson could be Graphing Native American Populations found at
/
  • P. 154 It’s in the Bag! Graphing Collection Bags

Unit Three: Fraction Concepts and Operations

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.NS.4 /
  • GCF of two whole numbers < or = to 100
  • LCM of two whole numbers < or = 12
  • Distributive property to show a sum of 2 whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor
/ 7.4 /
  • Focus on using the distributive property to show a sum of 2 whole numbers
/
  • HC p. 170B Early Finishers (game)
  • Marilyn Burns Lessons for Extending Multiplication Ch. 9 p. 103 Two Ways to Count to Ten, p. 161 Additional Activities
  • Marilyn Burns p. 202 “The Factor Game”
  • Marilyn Burns Math and Literature Grades 4-6 Two Ways to Count to Ten p. 191
  • 5th Grade Math Additional Activities and Resources for Harcourt Unit 5 Number Theory and Fractions Days 2-7

6.NS.1 /
  • Interpret, compute, and solve word problems about dividing fractions by fractions
/ 10.4
10.5 /
  • 10.4 and 10.5 focus on the standard algorithm. The focus here is to interpret, compute, and model division of fractions. Use problems from these two lessons after MB lessons for additional practice of students modeling their solution.
/
  • Marilyn Burns Lessons for Multiplying and Dividing Fractions, Grades 5-6 Ch. 11Division with Remainders p. 111, Ch. 12 Tool Kit for Dividing Fractions p. 123

Not represented in Common Core:
7.1
7.2
7.3
7.5
8.1
8.2
8.3
8.4
Ch. 9
10.1
10.2
10.3
10.4
10.5
10.6
10.7

Unit Four: Algebra Expressions, Equations, and Patterns

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.EE.2
6.EE.4
6.EE.7 /
  • Write variable expressions
  • Read and identify expressions using mathematical terms
  • Evaluate variable expressions paying attention to Order of Operations
  • Simplify expressions with like terms
  • Write and solve equations
/ 11.1
11.2 /
  • HC p. 258B Alternative Teaching Strategy
  • HC 11.1 Challenge worksheet
  • P. 260B Alternative Teaching Strategy, Writing in Mathematics, Advanced Learners

6.EE.1 /
  • Write and evaluate numerical expressions with whole number exponents
/ 11.3
11.4 /
  • Add supplemental activities with exponents > 2.
/
  • HC p. 266B Alternative Teaching Strategy, Early Finishers

6.EE.5
6.EE.7
6.EE.8 /
  • Understand solving an equation or inequality
  • Use substitution
  • Write and solve equations
  • Write inequalities
/ 12.1
12.2
12.3
12.4
12.5
13.1
13.2
13.3
13.4
13.5 /
  • Make sure students are writing and not graphing inequalities.
/
  • HC p. 274B Alternative Teaching Strategy, 12.1 reteach and challenge worksheets
  • 12.2 Math Lab
  • HC p. 277B Alternative Teaching Strategy
  • 12.3 reteach worksheet
  • HC p. 300B Consumer Connection

6.EE.9 /
  • Use variables to represent two quantities
  • Equations
/
  • IEFA LESSON addresses this standard

Not represented in Common Core: CHAPTER 14

Unit Five: Geometry and Plane Figures is not represented in Common Core.

Unit Six: Measurement: One and Two Dimensions

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.RP.3 /
  • Use ratio reasoning to convert measurement units
/ 19.1
19.2 /
  • 19.1 and 19.2 focus on customary and metric measurements but lack the ratio reasoning piece. In order to hit this standard, we have to supplement these ideas with the additional resources.

6.G.1 /
  • Area of right triangles by composing into rectangles or decomposing into triangles and other shapes
  • Area of other triangles by composing into rectangles or decomposing into triangles and other shapes
  • Area of special quadrilaterals by composing into rectangles or decomposing into triangles and other shapes
  • Area of polygons by composing into rectangles or decomposing into triangles and other shapes
/
  • This standard can be met in the IEFA lesson about the Cheyenne Morning Star if teachers extend the lesson further by finding the area of the Morning Star as well as other designs students create. This lesson was modeled in the 2010-2011 school year by the instructional coaches.
  • Another IEFA example lesson could be Estimating the Area of a Reservation found at
/
  • HC 21.2 p. 462B Alternative Teaching Strategy- place less emphasis on the estimation and more on finding the area. Expand to include right triangles, triangles, special quadrilaterals, and polygons.
  • Marilyn Burns About Teaching Mathematics Geometry activities “The Tangram Puzzle” p. 83
  • HC 21.2 p. 462B Visual Arts Connection

Not represented in Common Core:
19.3
19.4
19.5
19.6
Ch. 20
21.1, 21.3-21.5

Unit 7: Solid Figures and Measurement

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.G.4 /
  • Nets
  • Surface area
/ 23.1 /
  • Stretch this lesson over a 3 day period. Ensure students have the surface area concept mastered before moving into volume.
  • You are responsible for teaching an IEFA lesson for this standard.

6.G.2 /
  • Volume of a right rectangular prism with fractional edge lengths
  • Pack the prism with unit cubes
  • Apply the volume formula after the hands-on piece
/ 23.2 Math Lab
23.3 /
  • Marilyn Burns Sizing Up Measurement 3rd-5th grade p. 122 “Filling Boxes” (use fractional edge lengths on the boxes)

Not represented in Common Core:
Ch. 22
23.4
23.5
23.6

Unit 8: Ratio, Proportion, Percent, and Probability

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.RP.1 /
  • Ratios
/ 24.1 /
  • Marilyn Burns Sizing Up Measurement Grades 6-8 “Hello, Proportions” teach the beginning part of this comparing ratios to analogies.

6.RP.2 /
  • Rates
/ 24.1 /
  • Marilyn Burns Sizing Up Measurement Grades 6-8 p. 112 “Exploring Rates”

6.RP.3 /
  • Ratios
  • Equivalent ratios (proportions)
  • Proportional relationships
  • Use ratio and rate reasoning to:
-Make tables
-Solve unit rate problems
-Find percent of a quantity as a rate per 100
-Convert measurement units / 24.1
24.2
24.3
24.6
24.7
25.1
25.2 /
  • In order to solidify the understanding of percents, remind them that percent means “per one hundred” or out of one hundred. 6th grade Every Day Counts: Algebra Readiness is a great resource to teach this concept.
/
  • Marilyn Burns Sizing Up Measurement Grades 6-8 p. 116 “Hello, Proportions” finish this lesson from the ratios lesson.

Not represented in Common Core:
24.4
24.5
25.3-25.6
Ch. 26
Ch. 27

Unit 9: Algebra: Integers and Graphing

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
6.NS.5 /
  • Integers (positive and negative numbers)
/ 28.1
6.NS.6 /
  • Rational Numbers
-Recognize opposites
  • Ordered pairs on the coordinate plane
  • Number lines
/ 28.1
28.2
28.3
6.NS.7 /
  • Ordering and absolute value of rational numbers
/ 28.1
28.2
28.3 /
  • Make sure to include a lesson about interpreting statements of inequality as statements about the relative position of two numbers on a number line.

6.NS.1 /
  • Interpret and compute quotients of fractions
  • Dividing fractions by fractions
  • Using visual fraction models
/ 29.6 /
  • Use fraction problems from this lesson to create word problems for dividing fractions.
  • Use fraction problems from this lesson to have students create word problems for dividing fractions.
/
  • Marilyn Burns Lessons for Dividing Fractions
  • Further extensions can be found in the lesson Model for Dividing Fractions- Grade 6 at

6.NS.6
6.NS.8 /
  • Ordered pairs on the coordinate plane
  • Four quadrants
/ 30.1 /
  • You are responsible for teaching an IEFA lesson for this standard. An example lesson could be Stars in the Sky found at

Not represented in Common Core:
28.4
29.1
29.2
29.3
29.4
29.5
30.2
30.3

Standards not represented in Harcourt:

6.G.3

Standards that are represented by less than 3 lessons:

6.NS.2- needs 1

6.NS.5- needs 2

6.NS.8- needs 1

6.EE.4- needs 2

6.EE.6- needs 2

6.EE.9- needs 2

6.RP.1- needs 1

6.RP.2- needs 1