Math Curriculum Guide th
5 Grade 2012 – 2013 School Year
Dear Colleague, Please use this curriculum guide to assist in your planning of mathematical instruction during the school year. The included unit/topic plans are aligned with the New York State Common Core State Standards (CCSS) and utilize the enVision resources to uncover these understandings. In addition to this curriculum guide, it is recommended that you utilize the grade level calendar to pace your lessons and units of instruction. Although specific lessons and standards are listed per date, it is not required that this be strictly followed per day. Adjustments in your pacing may occur based upon your school’s alternate schedules and your particular student’s needs. The CCSS are divided into standards that are major priorities, supporting topics and additional topics. This highlighting scematic (bold and/or italics) will be utilized within each unit to identify these differences. All included lessons are required to be taught; however, emphasis should be placed on ensuring a full understanding of the major priorities. Assessments should mirror this hierarchy of priorities as well. When reviewing these curriculum guides, please note the included essential questions, both per topic and lesson. These were developed with the intent of sharing with your students. Consider posting these questions for students to become immersed in and as a means of keeping the class conversation focused on the objective of the period or unit as a whole. Additionally, please take advantage of the space provided on each page for you to include your own notes. Knowing that we are in the beginning phases of implementing the CCSS, along with utilizing the enVision resources, it is imperative that we consistently reflect upon on our practice, and consider various approaches and strategies to provide an optimal learning environment for all of our students to become successful. Please continue collaborating with your colleagues to work towards achieving this goal. Finally, you will notice during the post assessment time period, that some of the major priority standards have been included again as a plan of instruction. This will provide you with time to delve more deeply into these already discussed concepts. In planning student experiences, consider utilizing the center activities, problem solving questions, ExamView generated worksheets, or any other resources that you have found valuable pertaining to these concepts. The following symbol * has been included in the teacher notes column for each of the lessons that might reappear during this post assessment time period. Be proactive and put aside resources that you could use during this time period. Have an excellent 2012 – 2013 school year!
HHH Math 5 Curriculum Guide Unit/Topic 1: Place Value How does a digit’s position affect its value? How are whole numbers and decimals written, compared, and ordered? Lesson Number and Title
Common Core State Standard(s)
Weeks of Sept. 3 & Sept. 10 : 7 Days
Essential Question(s)
Teacher Notes
* 1-1
Place Value
5.NBT.1
How can you read and write large numbers?
1-2
Tenths and Hundredths
5.NBT.3.a
How can you write a fraction as a decimal?
Focus on the shift in Standard 5.NBT.1. Use Another Example on page 6 to develop the understanding of place value patterns.
* Assess the readiness of students prior to this unit. Lessons 1-2 and 1-3 may be combined. 1-3
Thousandths
5.NBT.1
How can a fraction showing thousandths be expressed as a decimal?
1-4
Decimal Place Value
5.NBT.3.a
How can you represent a decimal in a place value chart?
1-5
Comparing and Ordering Decimals
5.NBT.3.b
How can you compare and order decimals?
1-6
Problem Solving: Look For A Pattern
5.NBT.3
How can you use information organized on a grid to help find a pattern?
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HHH Math 5 Curriculum Guide Unit/Topic 2: Adding and Subtracting Decimals Weeks of Sept. 10 & Sept. 17, Sept. 24, Oct 1: 9 Days How can sums and differences of decimals be estimated? What are the standard procedures for adding and subtracting whole numbers and decimals? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes * For Topic 2, focus on developing a deep understanding of the relationship between addition and subtraction, not just on the procedure.
2-1
Mental Math
5.NBT.7
How can you use mental math to find sums and differences of decimals?
2-2
Rounding Whole Numbers and Decimals
5.NBT.4
How can you round whole numbers and decimals?
2-3
Estimating Sums and Differences
5.NBT.7
How can you estimate to find sums and differences?
2-4
Modeling Addition and Subtraction of Decimals
5.NBT.7
How can you use a grid to add and subtract decimals?
2-5
Problem Solving: Draw a Picture and Write an Equation
5.NBT.7
How can you draw a picture to help you choose an operation?
2-6
Adding Decimals
5.NBT.7
How can you add decimals?
2-7
Subtracting Decimals
5.NBT.7
How can you subtract decimals?
2-8
Problem Soving: MultipleStep Problems
5.NBT.7
How can you solve problems that require more than one step?
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HHH Math 5 Curriculum Guide Unit/Topic 3: Multiplying Whole Numbers Weeks of Oct. 1, Oct. 8, Oct. 15: 10 days What are the standard procedures for estimating and multiplying whole numbers? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
*
3-1
Multiplication Properties
5.NBT.6
What are the properties of multiplication?
3-2
Using Mental Math to Multiply
5.NBT.2
How can you use mental math to multiply by multiples of 10, 100 and 1,000?
3-3
Estimating Products
5.NBT.5
How can you estimate products?
3-4
Exponents
5.NBT.2
How can you use exponents to represent repeated multiplication of the same number?
*
3-5
Distributive Property
5.NBT.5
How can you use the Distributive Property to write two equal expressions?
*
3-6
Multiplying by 1-Digit Numbers
5.NBT.5
How do you multiply by 1-digit numbers?
3-7
Multipling 2-Digit by 2Digit Numbers
5.NBT.5
How do you multiply by 2-digit numbers?
3-8
Multiplying Greater Numbers
5.NBT.5
How do you multiply 3-digit numbers by 2-digit numbers?
3-9
Draw a Picture and Write an Equation
5.NBT.5
How can you draw a picture to help choose an operation?
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HHH Math 5 Curriculum Guide Unit/Topic 4: Dividing by 1-Digit Divisors What is the standard procedure for division and why does it work? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Oct. 15, Oct. 22: 8 days
Teacher Notes
4-1
Dividing Multiples of 10 and 100
5.NBT.6
How can you use mental math to divide multiples of 10 and 100?
*
4-2
Estimating Quotients
5.NBT.6
How can you use compatible numbers to estimate quotients?
4-3
Problem Solving: Reasonableness
5.NBT.6
How can you check that your answer is reasonable?
4-4
Connecting Models and Symbols
5.NBT.6
How can you use models and symbols to understand and record division?
*
4-5
Dividing by 1-Digit Divisors
5.NBT.6
When you divide a 3-digit number by a 1-digit number, how do you know where to put the first digit in the quotient?
*
4-6
Zeros In the Quotient
5.NBT.6
When do you write a zero in the quotient?
4-7
Problem Solving: Draw a Picture and Write an Equation
5.NBT.6
How can you draw a picture to help choose an operation?
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HHH Math 5 Curriculum Guide Unit/Topic 5: Dividing by 2-Digit Divisors What is the standard procedure for dividing with 2-digit divisors? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Oct. 29, Nov. 5: 9 days
5-1
Using Patterns To Divide
5.NBT.6
How can patterns help you divide large multiples of 10?
5-2
Estimating Quotients With 2-Digit Divisors
5.NBT.6
How can you use compatible numbers to estimate quotients?
5-3
Connecting Models and Symbols
5.NBT.6
How can you use arrays to model multi-digit division?
5-4
Dividing by Multiples of 10
5.NBT.6
How do you divide by a multiple of 10?
5-5
1-Digit Quotients
5.NBT.6
What are the steps for dividing by 2-digit numbers?
5-6
2-Digit Quotients
5.NBT.6
How can you divide larger numbers?
5-7
Estimating and Dividing With Greater Numbers
5.NBT.6
How can you solve problems involving division of larger numbers?
5-8
Problem Solving: Missing or Extra Information
5.NBT.6
How do I identify missing information in a word problem?
Teacher Notes
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HHH Math 5 Curriculum Guide Unit/Topic 6: Multiplying Decimals Weeks of Nov. 12, Nov. 19: 6 days What are the standard procedures for estimating and finding products involving decimals? Lesson Number and Title
6-1
Multiplying Decimals by 10,100 or 1,000
Common Core State Standard(s)
Essential Question(s)
5.NBT.2
What is the rule for multiplying decimals by 101, 102, 103?
Teacher Notes
*
6-2
Estimating the Product of a Decimal and Whole Number
Teach lessons 16-1 and 16-2 on the same day. 5.NBT.7
What are some ways to estimate products with decimals?
6-3
Number Sense: Decimal Multiplication
5.NBT.7
How can number sense be used to determine the location of decimal points in decimal multiplication calculations?
6-4
Models for Multiplying Decimals
5.NBT.7
How can you multiply whole numbers and decimals?
6-5
Multiplying a Decimal by a Whole Number
5.NBT.7
How do you multiply a decimal by a whole number?
6-6
Multiplying Two Decimals
5.NBT.7
How can you multiply two decimals?
6-7
Problem Soving: Multiple Step Problems
5.NBT.7
How can you solve multiple-step problems?
* Develop a deeper understanding of using estimation to decide decimal placement in a product. *
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* If time permits, lesson 6-7 can be included on the day of the topic 6 assessment.
HHH Math 5 Curriculum Guide Unit/Topic 7: Dividing Decimals Weeks of Nov. 26, Dec. 3: 8 days What are the standard procedures for estimating and finding quotients involving decimals? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
7-1
Dividing Decimals by 10,100, or 1,000
5.NBT.2
How can you divide decimals by 10, 100, and 1,000?
7-2
Estimating Decimal Quotients
5.NBT.7
How can numbers in division calculations be changed to other numbers that are easy to compute with mentally?
7-3
Number Sense: Decimal Division
5.NBT.7
How can you use reasoning to correctly place the decimal point in the quotient?
7-4
Dividing by a Whole Number
5.NBT.7
How can you divide a decimal by a whole number?
7-5
Dividing a Whole Number by a Decimal
5.NBT.7
How can you divide a whole number by a decimal?
7-6
Dividing a Decimal by a Decimal
5.NBT.7
How can you divide a decimal by another decimal?
7-7
Problem Soving: Multiple Step Problems
5.NBT.7
How do you solve multiple-step problems?
Teacher Notes
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* Develop a deeper understanding of using estimation to decide decimal placement in a quotient.
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HHH Math 5 Curriculum Guide Unit/Topic 8: Numerical Expressions, Patterns, and Relationships How are the values of an algebraic expression and a numerical expression found? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Dec. 3, Dec. 10, Dec. 17: 11 Days
8-1
Using Variables to Write Expressions
5.OA.2
How can you write an algebraic expression?
8-2
Order of Operations
5.OA.1
How can you evaluate a numerical expression containing more than one operation?
8-3
Simplifying Expressions
5.OA.1
What order should you use when you simplify an expression?
8-4
Evaluating Expressions
5.OA.1
How can you use the order of operations to evaluate expressions with decimals?
8-5
Addition and Subtraction of Expressions
5.OA.3
How can you find a rule and write an addition and subtraction expression?
8-6
Multiplication and Division Expressions
5.OA.3
How can you find a rule and write a multiplication and division expression?
8-7
Patterns: Extending Tables
5.OA.3
How can you find the relationship between two sequences?
8-8
Variables and Expressions
5.OA.2
How can you translate words into expressions?
8-9
Problem Solving: Act It Out and Use Reasoning
5.OA.2
How can you act out a problem and use reasoning to solve it?
Teacher Notes
HHH Math 5 Curriculum Guide Unit/Topic 9: Adding and Subtracting Fractions Weeks of Dec. 31, Jan. 7, Jan. 14: 11 Days What does it mean to add and subtract fractions with unlike denominators? What is a standard procedure for adding and subtracting fractions with unlike denominators? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
9-1
Equivalent Fractions
5.NF.1
How can you find equivalent fractions?
9-2
Fractions in Simplest Form
5.NF.1
How can you write a fraction in simplest form?
9-3
Problem Solving: Writing To Explain
5.NF.2
How do you write a math explanation?
9-4
Estimating Sums and Differences of Fractions
5.NF.2
How can you estimate the sum or difference of two fractions?
9-5
Common Multiples and Least Common Multiples
5.NF.1
How can you find common multiples of two numbers?
9-6
Finding Common Denominators
5.NF.1
How can you find common denominators for fractions with unlike denominators?
9-7
Adding Fractions With Unlike Denominators
5.NF.1
How can you add fractions with unlike denominators?
9-8
Subtracting Fractions with Unlike Denominators
5.NF.1
How can you subtract fractions with unlike denominators?
9-9
More Adding and Subtracting Fractions
5.NF.1
How can adding and subtracting fractions help you solve problems?
9-10
Problem Solving: Draw a Picture and Write and Equation
5.NF.2
What operation is needed to solve a problem with fractions?
Teacher Notes
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HHH Math 5 Curriculum Guide Unit/Topic 10: Adding and Subtracting Mixed Numbers What does it mean to add and subtract mixed numbers? What is a standard procedure for adding and subtracting mixed numbers? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Jan. 14, Jan. 21, Jan. 28: 8 Days
Teacher Notes
10-1
Improper Fractions and Mixed Numbers
5.NF.1
How can you represent quantities that are greater than or equal to 1?
*
10-2
Estimating Sums and Differences of Mixed Numbers
5.NF. 2
How can you use a number line to round fractions and mixed numbers to estimate their sums or differences?
*
10-3
Modeling Addition and Subtraction of Mixed Numbers
5.NF.3
How do you use models to add mixed numbers?
10-4
Adding Mixed Numbers
5.NF.1
How can you add mixed numbers?
10-5
Subtracting Mixed Numbers
5.NF.1
How can you subtract mixed numbers?
10-6
More Adding and Subtracting Mixed Numbers
5.NF.1
How can you add and subtract mixed numbers to solve problems?
10-7
Problem Solving: Draw a Picture and Write and Equation
5.NF.1
How can you draw a picture to help write an equation?
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HHH Math 5 Curriculum Guide Unit/Topic 11: Multiplying and Dividing Fractions and Mixed Numbers Weeks of Jan. 28, Feb. 4, Feb. 11: 12 Days What are standard procedures for estimating and finding products and quotients of fractions and mixed numbers? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes *
11-1
Fractions and Division
5.NF.3
How are fractions related to division?
11-2
Multiplying Fractions and Whole Numbers
5.NF.4.a
How can you multiply fractions and whole numbers?
11-3
Estimating Products
5.NF.5.a
How can you use compatible numbers to estimate with fractions?
11-4
Multiplying Two Fractions
5.NF.4.a
How can you multiply fractions?
11-5
Area of a Rectangle
5.NF.4.b
How can you find the area of a rectangle?
11-6
Multiplying Mixed Numbers
5.NF.4.a
How can you multiply mixed numbers?
11-7
Multiplication as Scaling
5.NF.5.b
How does multiplying by a fractions change the second factor?
11-8
Problem Solving: Multiple-Step Problems
5.NF.6
How can you solve multiple-step problems?
11-9
Dividing Whole Numbers by Unit Fractions
5.NF.7.b
How do you divide a whole number by a fraction?
11-10
Dividing Unit Fractions by Non-Zero Whole Numbers
5.NF.7.c
How can you model dividing a unit fraction by a whole number?
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11-11
Problem Solving: Draw a Picture and Write an Equation
5.NF.7.a
How can drawing a picture and writing an equation help you solve a problem.
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* * Read through math background and teacher notes prior to teaching the lesson. *
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HHH Math 5 Curriculum Guide Unit/Topic 12: Volumes of Solids Weeks of Feb. 11, Feb. 25, March 4: 8 Days How can 3-dimensional shapes be represented and analyzed? What does the volume of a rectangular prism mean and how can it be found? Lesson Number and Title
12-1
Solids
Common Core State Standard(s)
Essential Question(s)
5.MD.3
How do you describe a 3-dimensional shape or solid?
Teacher Notes
If you prefer to begin Topic 12 after the February break, teach lessons 12-1 and 12-2 on the same day. 12-2
Views of Solids
5.MD.3.a
How can you get information about a solid from different views?
12-3
Problem Solving: Use Objects and Solve a Simpler Problem
5. MD.5
How can you use a simpler problem to solve another problem?
12-4
Models and Volume
5.MD.3.a 5.MD.3.b
How can you use models to find the volume of a rectangular prism?
12-5
Volume
5.MD.5.a 5.MD.5.b
How can you find the volume of a rectangular prism?
12-6
Combining Volumes
5.MD.5.c
How can you use volume formulas to solve problems?
12-7
Problem Solving: Use Objects and Reasoning
5.MD.4
How can you use objects to solve problems?
HHH Math 5 Curriculum Guide Unit/Topic 13: Units of Measure What are customary measurement units and how are they related? What are metric measurement units and how are they related? Lesson Number and Title
Common Core State Standard(s)
Weeks of March 4, March 11: 8 Days
Essential Question(s)
13-1
Converting Customary Units of Length
5.MD.1
How can you change from one customary unit of length to another?
13-2
Converting Customary Units of Capacity
5.MD.1
How do you change from one unit of capacity to another?
13-3
Converting Customary Units of Weight
5.MD.1
How can you convert between customary units of weight?
13-4
Converting Metric Units of Length
5.MD.1
How can you convert metric units of length?
13-5
Converting Metric Units of Capacity
5.MD.1
How do you convert metric units of capacity?
13-6
Converting Metric Units of Mass
5.MD.1
How can you convert between metric units of mass?
13-7
Problem Soving: MultipleStep Problems
5.MD.1
How do you find hidden questions to solve multiple-step problems?
Teacher Notes
HHH Math 5 Curriculum Guide Unit/Topic 14: Data How can line plots be used to represent data and answer questions? How can numbers be used to describe certain data sets?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
14-1
Line Plots
5.MD.2
How can you organize data in a line plot?
14-2
Data From Surveys
5.MD.2
How can you display the data collected in a survey?
14-3
Making Line Plots
5.MD.2
How can you organize and represent measurement data?
Week of March 18: 5 days
Teacher Notes
Teach Lessons 14-3 and 14-4 on the same day.
14-4
Measurement Data
5.MD.2
How can we solve problems involving measurement data?
14-5
Problem Solving: Writing To Explain
5.G.2
How do you write a good math explanation?
HHH Math 5 Curriculum Guide Unit/Topic 15: Classifying Plane Figures Weeks of March 25, April 1: 6 Days How can angles be measured and classified? How can polygons, triangles and quadrilaterals be described, classified and named? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
15-1
Polygons
5.G.3
How do you classify polygons?
15-2
Triangles
5.G.3
How do you classify triangles?
15-3
Properties of Quadrilaterals
5.G.3
How do you classify quadrilaterals?
15-4
Special Quadrilaterals
5.G.3
Which shapes are special cases of another shape?
15-5
Classifying Quadrilaterals
5.G.4
How are special quadrilaterals related to each other?
15-6
Problem Solving: Make and Test Generalizations
5.G.3
How can you test generalizations?
Teacher Notes
The assessment for Topic 15 should be combined with the assessment for Topic 16, if possible.
Post Assessment Units of Instruction HHH Math 5 Curriculum Guide Unit/Topic 16: Coordinate Geometry How are points graphed? How can we show the relationship between sequences on a graph? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of April 29th & May 6th: 6 days
16-1
Ordered Pairs
5.G.1
How do you name and graph points on a coordinate grid?
16-2
Distances on a Coordinate Plane
5.G.1
How can you find the horizontal or vertical distance between two ordered pairs?
16-3
Problem Soving: Solve a Simpler Problem
5.G.1
What operation is needed to solve a problem?
16-4
Patterns and Graphing
5.G.2
How can you use coordinate grids to show mathematical relationships?
16-5
More Patterns and Graphing
5.G.2
How can you use coordinate grids to show a mathematical relationship?
16-6
Problem Solving: Work Backward
5.G.1
How can you work backwards to solve a problem?
Teacher Notes
HHH Math 5 Curriculum Guide Unit/Topic 17: Grade Level Priorities
Weeks of May 6, May 13 & May 19: 11 Days
Lesson Number
Common Core State Standard(s)
Essential Understanding(s)
1-1, 1-3,
5.NBT.1
Patterns can be used to mentally multiply decimals by 10, 100, and 1,000
3-2, 3-4, 6-1, 7-1
5.NBT.2
Place value patterns can be used to mentally divide decimals by 10,100, and 1,000.
1-2, 1-4, 1-5, 1-6,
5.NBT.3.a-b
Read, write, and compare decimals to thousandths.
2-2
5.NBT.4
Use place value understanding to round decimals to any place.
3-3, 3-5, 3-6, 3-7, 3-8, 3-9
5.NBT.5
Multiply multi-digit numbers fluently.
5.NBT.6
Division of numbers with up to 4-digit dividends and 2-digit divisors.
5.NBT.7
Add, subtract, multiply and divide decimals to hundredths.
5.NF.1
Add and subtract fractions with unlike denominators (including mixed numbers).
9-3, 9-4, 9-10, 10-2,
5. NF.2
Solving word problems involving addition and subtractions of fractions.
10-3, 11-1,
5.NF. 3
11-2, 11-4, 11-5, 11-6
5.NF.4.a-b
11-3, 11-7
5.NF.5.a-b
11-8
5.NF.6
11-9, 11-10, 11-11
5.NF.7.a-c
3-1, 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7, 5-8 2-1, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7 9-1, 9-2, 9-5, 9-6, 9-7, 9-8, 9-9, 10-1, 10-4, 10-5, 10-6, 10-7
A fraction describes the division of a whole into equal parts. Interpret a fraction as division of the numerator by the denominator. Multiply a fraction or a whole number by a fraction, which comes from multiplying by the numerator and dividing by the denominator. Find the area of a rectangle with fractional side lengths. Understand multiplication by a factor between 0 and 1 results in a smaller value. Understand multiplication by a factor greater than 1 results in a larger value. Solve real world problems involving multiplication of fractions and mixed numbers. For example, use visual fraction models or equations to represent the problem. Understand and apply division of unit fractions by non-zero whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
Teacher Notes
HHH Math 5 Curriculum Guide Unit/Topic 18: Step Up To Sixth Grade Lesson Number and Title
ONLY IF TIME PERMITS
Common Core State Standard(s)
Essential Question(s)
17-1
Understanding Ratios
6.RP.1
What is a mathematical way to compare quantities?
17-2
Understanding Rates and Unit Rates
6.RP.2
Are there special types of ratios?
17-3
Equal Rations and Proportions
6.RP.3.a
How can you find equal ratios?
17-4
Using Ratio Tables
6.RP.3.a
How can you use ratio tables to solve proportion?
17-5
Comparing Rates
6.RP.3.b
How can you use unit rates to compare?
17-6
Multiplying with Zeros in the Product
6.NS.3
When do you insert zeros in the product?
17-7
Greatest Common Factor
6.NS.4
How can you find the GCF of a set of numbers?
17-8
Using Expressions To Describe Patterns
6.EE.2
How can you write expressions to describe patterns?
17-9
Properties of Operations
6.EE.3
How can you use properties of operations to rewrite expressions?
17-10
Surface Area
6.G.4
How can you find the surface area of a rectangular prism?
Remaining Days of School Teacher Notes