FifthGrade

**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: Use Whole Numbers and Decimals

*ATS = Alternative Teaching Strategy

*PA = Performance Assessment

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
NBT3 /
  • Read, write, and compare decimals to thousandths
  • Vocabulary: tenths, hundredths, thousandths, base ten numerals, expanded form, <, >, = (meaning of symbols)
/ 2.1
2.2
2.3 /
  • 2.2 ATS
  • 2.3 Advanced learners box
  • 3.5 ATS
  • Unit 1 technology link-up P. 91
  • Harcourt Intervention Skills Teacher’s Guide P. IN172-IN174

NBT4 /
  • Use place value to round decimals
  • Vocabulary: rounding
/ 3.2 /
  • May need to review rounding with whole numbers
  • Delete front-end estimation
/
  • 3.3 ATS
  • Harcourt Intervention Skills Teacher’s Guide P. IN164-IN166
  • Marilyn Burns- 50 Problem Solving Lessons, The Place Value Game (p.65)
  • Marilyn Burns- Lessons for Introducing Decimals and Percents, Benchmarks (p.83), Foreign Exchange Rounding (p.128), Pigs Will Be Pigs (p. 134)

NBT7 /
  • Use concrete models or drawings to use operations with decimals. Relate chosen strategy to written method and explain the reasoning used
/ 3.5 / *IEFA lesson on area (see implementation link) /
  • 3.5 ATS
  • 3.5 ATS scaffold
  • Harcourt Intervention Skills Teacher’s Guide P. IN176-IN178

NBT4 /
  • Use place value to round decimals
  • Vocabulary: rounding
/ 3.6 /
  • Delete front-end estimation

OA2 /
  • Write and interpret numerical expressions
  • Vocabulary: expression, evaluations, parenthesis, sum, product
/ 4.1
4.2 /
  • 4.1 Special needs (lesson opener)
/
  • 2.4 #5 and guiding practice
  • 4.1 Advanced learners
  • 4.1 Thinker’s corner
  • 4.2 ATS

NBT7 /
  • Use concrete models or drawings to use operations with decimals. Relate chosen strategy to written method and explain the reasoning used
/ 4.5 /
  • Unit 1 PA Task A P. 90

*Delete: 1.1, 1.2, 1.3, 1.4, 1.5, 3.1, 3.4, 3.7, 4.3, 4.4, 4.6

Unit Two: Data, and Graphing

  • Five lessons from this unit will be taught within Harcourt Unit 7.
  • The rest of the lessons within Unit 2 are not implicitly addressed in the Common Core Standards.
  • Data and graphing are important mathematical concepts, and are heavily addressed on the CRT and will need to be imbedded into science, social studies, language arts, and mathematics where appropriate.
  • Infuse data and graphing terminology as often as possible.

Unit 3: Multiply Whole Numbers and Decimals

*ATS = Alternative Teaching Strategy

*PA = Performance Assessment

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
NBT5 /
  • Multiply multi-digit whole numbers using standard algorithm
*Note: The lattice method should only be taught after students have a solid understanding of the place value involved with multiplication. / 7.3
7.4
7.5 / *CC 4th grade has heavy emphasis on understanding of multiplication BUT this year go through array, lattice, and multiple representations of multiplication /
  • Unit 3 challenge p. 183
  • Unit 3 PA Task A
  • Unit 3 P. 188
  • AIMS Area Codes *located in curriculum library (Directions for an array model on page 3)

NBT7 /
  • Use concrete models or drawings to use operations with decimals. Relate chosen strategy to written method and explain the reasoning used
/ 8.1 Hands-on
Reteach worksheet 8.1
8.3
8.2
8.4
8.5
8.6 / Teach modeling in lesson 8.3 before lesson 8.2.
In lesson 8.2, teach looking for patterns and using power of ten to “move” decimal point. /
  • Unit 3 PA task B
  • Unit 3 P. 188
  • Harcourt Intervention Skills Teacher’s Guide p. IN383

NBT2 /
  • Explain pattern in the number of zeros of the product when multiplying a number by powers of 10
/
  • Marilyn Burns-Extending Multiplication, Times 10 (p.164)

*Delete- 7.1, 7.2

Unit 4: Divide Whole Numbers and Decimals

*ATS = Alternative Teaching Strategy

*Pa = Performance Assessment

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
NBT6
(NBT1 lesson 10.1) /
  • Illustrate and explain finding whole number quotients by using equations, rectangular arrays, and/or area models
  • Recognize in a multi-digit number, a digit in one place represents ten times as much as the place to its right and 1/10 of the place on its left.
/ 9.2
9.3
9.4
9.5
10.1
10.2
10.3
10.4
10.5
10.6 /
  • CC 4th grade has a heavy emphasis on understanding division BUT this year before beginning any 5th grade Harcourt lessons, make sure students have a good foundation of the basics of division by providing concrete model lessons.
/
  • Chapter 13 Check what you know P. 275
  • Lessons for Introducing division by Marilyn Burns (Located in the curriculum library) to explore the basics of division.
  • Lesson for Extending Division Marilyn Burns- (Located in the curriculum library)
Lessons 1-6 to explore basics of division and lesson 11-17 to provide practice with long division
NBT7
(NBT1 11.1) /
  • Use concrete models or drawings to use operations with numbers. Relate the strategy chosen to a written method and explain the reasoning used.
  • Recognize that in a multi-digit number a digit in one place represents ten times as much as the place to its right and 1/10 of the place to its left.
/ 11.1
11.2
11.3
11.4 /
  • Unit 4 Challenge P. 267
  • Harcourt Intervention Skills Teacher’s Guidep. IN156

NF3 /
  • Interpret a fraction as division of the numerator by the denominator
/ 11.5 /
  • Every Day Counts

OA2 /
  • Write and interpret numerical expressions
/ 12.1 /
  • Unit 4, PA Task B P. 270

OA1 /
  • Use parenthesis, brackets, or braces to evaluate expressions
/ 12.2 /
  • Unit 4 technology link-up #5 P. 271

OA3 /
  • Generate two numerical patterns, identify relationships between terms, and form ordered pairs.
/ 12.3
12.4 /
  • 4.1 Advanced Learners P. 64B

NBT7 /
  • Use concrete models or drawings to use operations with numbers. Relate the strategy chosen to a written method and explain the reasoning used.
/ 12.5 /
  • Unit 4, PA Task B P. 270

NBT6 /
  • Illustrate and explain finding whole number quotients by using equations, rectangular arrays, and/or area models
/ 12.6
12.7 /
  • Chapter 13 Check what you know P. 275

*Delete- 9.1

Unit 5: Number Theory and Fractions

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
NBT.1
NBT.2 /
  • Recognize that a digit in one place represents ten times as much as it represents in the place to its right and one-tenth of what it represents in the place to its left.
  • Explain patterns when multiplying or dividing by powers of ten and zeros. (Decimals)
/ 14.2 /
  • Unit 5 Challenge P. 337

NF.3 /
  • Interpret a fraction as division of the numerator by the denominator.
/ 15.6

Unit 6: Operations with Fractions

*ATS = Alternative Teaching Strategy

*PA = Performance Assessment

*PS = Problem Solving

Common Core Standard / Emphasis / HB
Lesson / Additions/Deletions / Supplemental Resources
NF2 /
  • Use visual fraction models or equations to solve real-world addition and subtraction of fractions problems, and use benchmark fractions and number sense of fractions to assess the reasonableness of answers.
/ 16.1
16.3
16.4
16.6
17.2
17.3
17.4
17.5 / Need: Problems with answers given for students to justify and evaluate.
Example from Harcourt: P. 358 # 45 and # 46
*Give any problem with a correct or incorrect answer and have students justify their reasoning for being correct or incorrect. /
  • 16.1 ATS P. 346B
  • 16.3 Benchmark
  • 16.5 P. 358
  • 17.1 PS worksheet
  • Unit 6 PS P. 424
  • Harcourt Family Involvement Activities FA12

NF1 /
  • Replace given fractions with equivalent fractions to add and subtract fractions with unlike denominators (Including mixed numbers)
/ 16.5
16.6
16.2
17.1
17.2
17.3
17.4 / For lesson 16.5, least common denominator must be taught as a prerequisite skill
For lesson 17.1, least common denominator must be taught as a prerequisite skill /
  • 16.4 Strategy
  • 17.1 ATS P. 370 Scaffold Instruction
  • Lessons for Extending Fractions Marilyn Burns Lessons 9-14, Pizza Problem (page 178), Does 2/1 -10/6 =1/3 (page 185)

NF4
NF6 /
  • Interpret product (a/b) x q as parts of a partition of q into b = parts.
  • Use visual fraction models and equations to represent real-world problems involving multiplication of fractions and mixed-numbers.
/ 18.1
18.2
18.3
18.4
18.5 /
  • Teach lesson 18.2 BEFORE 18.1
  • For lesson 18.1 teach using models instead of multiplying straight across. Make sure students are able to explain the process using numbers, pictures, and words. Also stress the meaning of the symbols (1/2 x 1/3 means “one-half of one-third is the same as one-sixth” as shown in models.
/
  • Unit 6 P. 418
  • Unit 6 PS P. 424
  • Marilyn Burns Lessons for Multiplying and Dividing Fractions Lessons 2-6. {Chapt 2 (p.11), Chapt 3 (p.23), An Experiment with Mice (p.155)
  • Rusty Bressar and Carin Holtzman Developing Number Sense, Trail Mix for a Crowd (p.67)

NF7 /
  • Interpret division on a unit fraction by a non-zero whole number and compute quotients. Interpret division of a whole number by a unit fraction and compute such quotients. Solve real-world problems using both of the above criteria.
/ 19.1
19.3
19.5 /
  • Teach meaning of division of whole numbers by fractions using visual models instead of explicitly teaching reciprocals.
  • For lesson 19.3, teach first part of lesson that includes the visual lesson.
/
  • Before teaching Harcourt lessons begin with Marilyn Burns-Lessons for Multiplying and Dividing Fractions lessons 7-10, 12
  • Rusty Bressar-Math and Literature, Beasts of Burden (p.19), Sam Johnson and the Blue Ribbon Quilt (p.123)

NF5 /
  • Interpret multiplication as scaling
/
  • Marilyn Burns-Lessons for Multiplying and Dividing Fractions, Chapter 4 (p.33), Chapter 6 (p.57), Multiplying with Rectangles Prompt (p.143)
  • Rusty Bressar- Math and Literature, Grandfather Tang's Story (p.60), Jim and the Beanstalk (p.79)
  • Stephanie Sheffield..Math and Nonfiction, Ed Emberly's Picture Pie (p. 47), Icebergs and Glaciers (p.101)

*Delete-16.1, 19.2, 19.4

Unit 7: Geometry and Algebra

*PA = Performance Assessment

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
MD.2 /
  • Make a line plot to display a data set of measurements in fractions of a unit.
/ 5.1 /
  • Use as a prerequisite for building line plots with fractional numbers.
/
  • Chris Confer-Sizing Up Measurement, Creating Benchmarks for Height (p.28)
  • Stephanie Sheffield...-Math and Nonfiction, A More Perfect Union (p.138), Wilma United (p.192)

*CRT tested Item /
  • Bar graphs
  • Line graphs
/ 5.5 /
  • Look at data in a bar graph, determine what type of data is appropriate for a bar graph, and build a bar graph from the data.
  • Discuss properties of a line graph and uses. When reading a story context about a line graph, choose from a selection of graphs which best fits the information.
/
  • Display data and put into a bar graph. (Ex. Using the table above, create a bar graph for the information including labels.)
  • Line graph (Ex. Given a story context about Paul riding his bike home from school, which graph shows that he rode halfway, stopped to visit with a friend, and then continued home?)

G.1 /
  • Use ordered pairs to locate specific locations on a coordinate plane.
/ 6.2 /
  • Stephanie Sheffield...-Math and Nonfiction, Chimp Math (p.29), How Much, How Many, How Far...(p.97)
  • Marilyn Burns-A Collection of Math Lesson, A Geometry Lesson with Pentaminos (p.139)

*CRT tested item /
  • Line graphs
/ 6.3 /
  • Students need to analyze the graphs and discuss what type of change is happening over time. Students should ask questions, answer questions, and write questions about the graphs they look at.
/
  • 5th grade Variables science kit includes many opportunities for students to make and analyze line graphs.

*CRT tested item /
  • Bar graphs
/ 6.6 /
  • Look at data in a bar graph, determine what type of data is appropriate for a bar graph, and build a bar graph from the data.

G.3
G.4
*CRT tested item (properties of triangles) /
  • Understand logical relationships between categories and connecting subcategories of 2-D figures.
  • Classify 2-D figures in a hierarchy based on properties
  • *What are the properties of the different types of triangles?
/ 20.3
21.1
21.2 /
  • Always-Sometimes-Never Strategy by Harvey Silver (Ex. 1. Give students a list of statements 2. Have students identify which statements are always true, sometimes true, and never true 3. Have students justify and explain.)
  • Group and Label aka. Open or Closed sort Strategy by Harvey Silver (Ex. 1. Give a collection of heterogeneous items. 2. Have students group and label the data. 3. Justify and explain their sorts.)
  • Mini lessons for Math Practice by Math Solutions (Located in the literacy office) Guess my Rule
  • Rusty Bressar-Math and Literature, Marvelous Math (p.117), One Riddle, One Answer (p.167), Sam Johnson (p.123), The Warlord's Puzzle (p.203)

*CRT tested item /
  • Transformations
  • Vocabulary: translation, reflection, and rotation
/ 21.3 /
  • Marilyn Burns- Collection of Math Lessons, Geometry Lesson with Pentaminos (p.139)

G.1 /
  • Understand ordered pairs are used to locate specific locations on a coordinate plane.
/ 23.1
23.2 (Positive integers only) /
  • Leave out negative integers.
/
  • HB Writing in Mathematics P. 500B
  • Harcourt Intervention Skills Teacher’s Guide p. IN270-IN272
  • Harcourt Intervention Skills Teacher’s Guide p. IN371 (Use your own students as examples)
  • 4.1 Advanced Learners P. 64B

G.2
*CRT tested item (Transformations only in Quad. 1) /
  • Represent real-world and mathematical problems by graphing points and interpret coordinate values and points.
  • Transformations
/ 23.3 (Transform in Quad. 1 only)
23.4 (Quad. 1 only) /
  • Only use coordinates from quadrant 1.
/
  • Unit 7 PA P. 516 Task B

*Delete- rest of Unit 2 and 20.1, 20.2, 20.3, 20.4, 20.5, 20.6, 20.7, 21.3, 21.4, 21.5, 21.6, 22.1, 22.2, 22.3, 22.4

Unit 8: Measurement

*PS = Problem Solving

*ATS = Alternative Teaching Strategy

Common Core Standard / Emphasis / HB Lesson / Additions/Deletions / Supplemental Resources
MD.2 /
  • Measure objects to the nearest ½, ¼, 1/8 inch. Display data in a line plot.
  • Redistribute the measurements to find a mean.
/ 24.1 /
  • Once students measure a variety of objects to the nearest ½, ¼, 1/8 inch, put the data into a line plot. Discuss results and have students ask/answer questions about the data. (Ex. Add the total number of inches that measure to the nearest ½ inch.)
/ (Use the three lessons under MD4 grade 3 as a prerequisite.)
(Use two 5th grade MD2 lessons to supplement. These are great open ended questions.)
  • Chris Confer-Sizing Up Measurement, Creating Benchmarks for Height (p.28)
  • Stephanie Sheffield...-Math and Nonfiction, A more Perfect Union (p.138), Wilma Unlimited (p.192)

MD.1 /
  • Convert among different sized units and use those in solving multi-step real-world problems.
/ 24.3 /
  • Unit 4 PS P. 272-273
  • HB P. 530 #57
  • IEFA Reservation area lesson
  • Chris Confer-Sizing Up Measurement, How Long is a Line? (p.9), How Much is a Meter (p.14), Going Home (p.31), Stacks of Kids (p.35), Relationships in the Metric System (p.41), How Much Soda? (p. 117), Cook-a-Doodle-Doo! Granny's Magnificent Strawberry Shortcake Recipe (p.145), Fruit Salad (p. 190), The Fewest Weights (p.202), Metric Hunt (p.208), Classroom Decisions (p.222), Let's Go the Movies (p. 235), The Last Day of School (p.238)

*CRT tested item /
  • Converting among customary capacity
/ 24.4 /
  • Students should know how many cups in a pint, pints in a quart, etc.

MD.3 /
  • Recognize volume as an attribute of solid figures. Understand concepts of volume measurement.
/ 27.1 /
  • This is a big concept in 5th grade. Students need many experiences with volume, using models, and its attributes to understand its meaning before they use the algorithm. The suggested supplemental resources provides a large number of scaffolded lessons.
/
  • Sizing up Measurement grades 3-5 by Chris Confer and Math Solutions (Found in the curriculum library and literacy center) pp. 96 -148
  • ATS P. 594 scaffold instruction

*CRT tested Item /
  • Surface Area
/ 27.2 /
  • Use the net of a rectangular prism to find area of each separate surface as well as total surface area.

MD.4
MD.5 /
  • Measure volumes using a variety of units.
  • Relate volume to operations of multiplication and division within real-world problems about volume.
/ 27.3
27.4
27.5 /
  • 27.3 provides the algorithm for finding volume. Make sure students have a deep understanding of what volume is and its attributes before introducing the algorithm.
/
  • Sizing up Measurement grades 3-5 by Chris Confer and Math Solutions (Found in the curriculum library and literacy center) pp. 96 -148

*Delete- 24.1, 24.2, 24.4, 24.5, 24.6, 24.7, 25.1, 25.2, 25.3, 25.4, 26.1, 26.3, 26.4, 26.6, 27.2

Unit 9: Ratio, Percent, and Probability

*ATS = Alternative Teaching Strategy

Common Core Standard / Emphasis / Harcourt Lessons / Additions/Deletions / Supplemental Resources
NF.5 /
  • Interpret multiplication as scaling with whole numbers, proper fractions, and improper fractions.
/ 28.3
28.4 /
  • ATS p. 622B
  • Technology P. 622B
  • Early Finishers P. 622B
  • P. 623 #4 teaching sidebar Assess. Both questions can be used as discussion and writing in math.

A.3 /
  • Generate two numerical patterns, identify relationships between terms, and form ordered pairs.
/ 28.4
NF.3
NBT.4 (Repeating Decimals lesson from Marilyn Burns) /
  • Interpret a fraction as a division problem.
/ 29.3
29.4 /
  • Lessons for Extending Division grades 4-5 by Marilyn Burns (Found in the curriculum library) P. 65 “The Dividend Stays the Same”
  • Lessons for Decimals and Percents grades 5-6 by Marilyn Burns (Found in the curriculum library and literacy center) P. 94 “Relating Fractions and Decimals” and P. 103 “Introducing Repeating Decimals”

*Delete- 28.1, 28.2, 28.5, 29.1, 29.3, 29.5, 29.6, 30.1, 30.2, 30.3, 30.4, 30.5, 30.6