Math Curriculum Guide rd
3 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 Grade 3 Curriculum Guide Unit/Topic 1: Numeration How are greater numbers read and written? How can whole numbers be compared and ordered? How does a digit’s position affect its value?
Lesson Number and Title
Weeks of Sept. 3rd, 10th & 17th, 10 Days
Common Core State Standard(s)
Essential Question(s)
Teacher Notes ~Standard form ~Expanded form ~Word form
1-1
Numbers: Representing Numbers
3.NBT.1
How can you read and write 3-digit numbers?
1-2
Ways to Name Numbers
3.NBT.1
How can you name the same number in different ways?
1-3
Greater numbers
3.NBT.1 & 3.NBT.2
How can you read and write greater numbers?
1-4
Understanding number lines
3.NBT.1
How can you locate and write numbers on a number line?
1-5
Counting on a number line
3.NBT.1
How can you complete the pattern on a number line?
1-6
Comparing numbers
3.NBT.1
How can place value help you compare whole numbers?
1-7
Ordering Numbers
3.NBT.1
How can you order numbers?
1-8
Problem Solving: Making an organized list
3.NBT.2
How can you solve problems by making an organized list?
HHH Math Grade 3 Curriculum Guide Unit/Topic 2: Number Sense: Addition and Subtraction How can sums and differences be found mentally? How can sums and differences be estimated? In what ways can operations affect numbers? How can different strategies be helpful when solving a problem? How does a digit’s position affect its value?
Lesson Number and Title
2-1
Addition Meaning and Properties
2-2
Subtraction Meanings
2-3
Using Mental Math to Add
2-4
Using Mental Math to Subtract
2-5
Rounding
2-6
Estimating Sums
2-7
Estimating Differences
2-8
Making sense of addition and subtraction equations
2-9
Problem Solving: Reasonableness
Weeks of Sept. 24th & Oct. 1st, 8th: 13 days
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
3.NBT.2 3.OA.9
How can the addition properties be used to show relationships that always hold true?
**Spend 2-days. 2nd day teacher must use supplemental materials
3.NBT.2 3.NBT.2
3.NBT.2
3.NBT.1 3.NBT.2 3.NBT.1 3.OA.8 3.NBT.2 3.NBT.1 3.OA.8
3.NBT.2
3.NBT.2 3.OA.8
When do you subtract? How can you break apart numbers or make a ten to add 2digit numbers using mental math? When can you subtract with mental math?
How can you round numbers?
How can you estimate sums?
How can you estimate differences?
How can a pan balance help you think about equations?
How can you use reasonableness to justify an answer?
*
Understanding the value to the left of the = is the same as the value to the right.
*
HHH Math Grade 3 Curriculum Guide Unit/Topic 3: Using Place Value to Add and Subtract What are standard procedures for adding and subtracting whole numbers? How does a digit’s position affect its value?
Lesson Number and Title
Weeks of Oct. 15th, 22nd & 29th: 9 days
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
Adding in expanded form
3-1
Adding with an Expanded Algorithm
3.NBT.2
How can you break a large addition problems into smaller ones?
3-2
Models for Adding 3-Digit Numbers
3.NBT.2
How can you add 3-digit numbers?
3-3
Adding 3-Digit Numbers
3.NBT.2 3.OA.8 3.NBT.1
How can you use addition to solve problems?
3-4
Adding 3 or More Numbers
3.NBT.2 3.OA.8
How can you use addition to solve problems?
3-5
Problem-Solving: Drawing Pictures
3.NBT.2 3.OA.8
How can you solve a problem by drawing a picture?
3-6
Subtracting with an Expanded Algorithm
3.NBT.2
How can you break a large subtraction problem into smaller, simpler ones?
3-7
Models for Subtracting 3Digit Numbers
3.NBT.2 3.OA.8
How can you use models to subtract 3-Digit numbers with regrouping?
*
3-8
Subtracting 3-Digit Numbers
3.NBT.2 3.OA.8 3.NBT.1
How can you subtract 3-digit numbers using paper and pencil?
*
3-9
Subtracting Across Zeros
3-10
Problme Solving: Draw a Picture and Write a Number Sentence
3.NBT.2
3.NBT.2 3.OA.8
How can you subtract from a 3-digit numbers with zeros?
How can a picture help you write a number sentence?
*
*
Subtracting in expanded form
Spend 2 days on this topic, teachers supplement
*
HHH Math Grade 3 Curriculum Guide Unit/Topic 4: Meanings of Multicplication What are different meanings of multiplication? How are addition and multiplication related? In what ways can operations affect numbers? How can different strategies be helpful when solving a problem?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Nov 1st & 5th: 7 days
Teacher Notes
4-1
Multicplication as Repeated Addition
3.OA.1 3.OA.3 3.OA.5
How can you find the total number of objects in equal groups?
*
4-2
Arrays and Multiplcation
3.OA.1 3.OA.3 3.OA.5
What are arrays, and how do they show multiplication?
*
4-3
The Communative Property
3.OA.1 3.OA.3 3.OA.5
What happens when you multiply two numbers and than switch the order of the factors?
*
4-4
Writing Muplications Stories
3.OA.1 3.OA.3 3.OA.5
How can you write a story to describe a multiplication fact?
*
4-5
Problem Solving: Writing to Explain
3.OA.1 3.OA.3 3.OA.5 3.OA.9
How do you write a good mathematical explanation?
*
HHH Math Grade 3 Curriculum Guide Unit/Topic 5: Mupliplication Facts: Use Patterns What patterns can be used to find certain multiplication facts? In what ways can operations affect numbers? How can different strategies be helpful when solving a problem? How does a digit’s position affect its value?
Lesson Number and Title
5-1
5-2
5-3
5-4
2 and 5 Factors
9 as a Factor
Multiplying with 0 and 1
Patterns for Facts
5-5
10 as a Factor
5-6
Multiplying by Multiples of 10
5-7
Problem Solving: Two Question Problems
Weeks of Nov. 12th 19th & 26th: 9 days
Common Core State Standard(s)
Essential Question(s)
3.OA.3 3.OA.9 3.NBT.3
How can you use patterns to multiply by 2 and 5?
*
How can pattern be used to find 9 facts?
*
What are the patterns in multiples of 1 and 0?
*
What patterns can help you remember multiplication facts for 2 and 5?
*
What are the patterns in multiples of 10?
*
How can basic facts help us when we multiply a single-digit number by a multiple of 10?
*
How can you tell when you need to answer more than one question to solve a problem?
*
3.OA.3 3.OA.9 3.OA.7 3.OA.8 3.OA.3 3.OA.9 3.OA.8 3.OA.3 3.OA.9 3.OA.8 3.OA.3 3.OA.9 3.NBT.3 3.OA.8
3.NBT.3
3.OA.3 3.OA.8
Teacher Notes
HHH Math Grade 3 Curriculum Guide Unit/Topic 6: Multiplcation Facts: Use Known Facts How can unknown multiplication facts be found using known facts: In what ways can operations affect numbers? How can different strategies be helpful when solving a problem? Why does “what” we measure influence “how” we measure?
Lesson Number and Title
Weeks of Nov. 29th & Dec. 3rd: 9 Days
Common Core State Standard(s)
Essential Question(s)
How can the Distributive Property help you break apart an array to multiply with other facts?
6-1
The Distributive Property
3.OA.5 3.OA.3
6-2 & 6-3
3 as a Factor 4 as a Factor
3.OA.5 3.OA.3 3.OA.5 3.MD.7
6-4 & 6-5
6 and 7 as a Factor 8 as a Factor
3.OA.5 3.OA.3 3.MD.7
Teacher Notes
*
How can you break apart arrays to multiply by 3? How can you break apart arrays to multiply by 4?
*
How can you break apart arrays to multiply by 6 and?? How can you break apart arrays to multiply by 8?
*
How can you multiply 3 numbers?
*
3.OA.3 3.OA.8
How can you use strategies to multiply?
*
3.OA.5 3.OA.3 3.OA.5
6-6
Multiplying by 3 Factors
6-7
Multiplcation Facts
6-8
Multiplying to Find Combinations
3.OA.3
How can you find all the possible combinations?
*
6-9
Problem Solving: Multiple Step Problems
3.OA.3 3.MD.8
How can you figure out what question needs to be answered first in a multiple-step problem?
*
HHH Math Grade 3 Curriculum Guide Unit/Topic 7: Meanings of Division What are different meanings of division? How is division related to other operations? In what ways can operations affect numbers? How can different strategies be helpful when solving a problem?
Lesson Number and Title
Weeks of Dec. 12th & 17th: 8 days
Common Core State Standard(s)
Essential Question(s)
How can you think of division as sharing?
*
Teacher Notes
7-1
Division as Sharing
3.OA.2 3.OA.3 3.OA.4
7-2
Division as Repeated Subtractraction
3.OA.2 3.OA.3 3.OA.4
How can you think of division as repeated subtraction?
*
7-3
Finding Missing Numbers in a Multiplication Table
3.OA.6 3.OA.4 3.OA.9
How can you use a multiplication table to solve division problems?
*
7-4
Problem Solving: Choose an Appropriate Equation
How can you describe a problem situation using an equation?
*
7-5
Writing Division Stories
3.OA.3 3.OA.4
What kinds of stories involve division stories?
*
7-6
Problem Solving: Use Objects and Draw a Pciture
3.OA.6 3.OA.3 3.OA.4
How can you use objects and draw a picture to solve a problem?
*
3.OA.4 3.OA.6
HHH Math Grade 3 Curriculum Guide Unit/Topic 8: Division Facts How can an unknown division fact be found by thinking of a related multiplication fact? In what ways can operations affect numbers? How can different strategies be helpful when solving a problem?
Lesson Number and Title
8-1
Relating Multiplication and Division
8-2
Fact Families with 2, 3, 4, and 5
8-3
Fact Families with 6 and 7
8-4
Fact Families with 8 and 9
8-5
Problem Solving: Multiple-Step Problems
8-6
Making Sense of Multiplication and Division Equations
8-7
Dividing with 0 and 1
Common Core State Standard(s) 3.OA.3 3.OA.4 3.OA.7 3.OA.3 3.OA.4 3.OA.7
Weeks of Jan. 2nd & 7th: 9 days
Essential Question(s)
Teacher Notes
How are multiplication and division facts related?
*
How can you use multiplication to help you divide by 2, 3, 4, and 5?
*
3.OA.3 3.OA.7
How can you use multiplication to help you divide by 6 and 7?
*
3.OA.3 3.OA.7
How can you use multiplication to help you divide by 8 and 9?
*
How can you solve problems that involve more than one step?
*
How can a pan balance help you think about multiplication and division equations?
*
3.OA.3 3.OA.4 3.OA.5
What happens when you divide by 0 and 1?
*
8-8
Multiplication and Division Facts
3.OA.3 3.OA.4 3.OA.7
How can you use multiplication and division facts to solve problems?
*
8-9
Problem Solving: Draw a Picture and Write a Number Sentence
3.OA.3
How can you solve problems by drawing a picture and writing a number sentence?
*
3.OA.3 3.OA.4 3.OA.8 3.OA.3 3.OA.4
HHH Math Grade 3 Curriculum Guide Unit/Topic 9: Understanding Fractions What are differernt interpreations of a fraction? Why express quantities, measurements, and number relationships in different ways? In what ways can operations affect numbers? How can different strategies be helpful when solving a problem? Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Jan. 15th & 21st: 10 Days Teacher Notes
11-6 & 11-7
Combining and Separating Shapes Making New Shapes
3.G.1 3.G.2
What shapes can you combine to make hexagon? How can you use a square to make a pentagon?
11-8 & 11-9
Problem Solving: Solve a Simpler Problem & Make and Test Generalizations
3.G.1 3.G.2
How can you solve a simpler problem in order to solve a given problem? What generalization can be made from a group of polygons?
9-1
Dividing regions into equal parts
3.NF.1
How can you divide into two equal parts?
9-2
Fractions and Regions
3.NF.1
How can you write fractions to name part of a whole?
9-3
Fractions and Sets
3.NF.1
How can you write a fraction to name part of a set?
9-4
Fractional Parts of a Set
3.NF.1
How can you find a fractional part of a set?
9-5
Locating Fractions on the Number Line
3.NF.2.a 3.NF.2 3.NF.2.b
How can you find a fraction on a number line?
*
9-6
Benchmark Fractions
How can you estimate parts?
*
9-7
Fractions and Lengths
How can you write a fraction to name part of a length?
*
9-8
Problem Solving: Make a Table and Look for Pattern
3.NF.2.a
3.NF.2.b
3.0A.3
How can you use a pattern in a table to help you solve a problem?
HHH Math Grade 3 Curriculum Guide Unit/Topic 10: Fraction Comparison and Equivalence What are different ways to compare fractions? Why express quantities, measurements, and number relationships in different ways?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of Jan. 30th & Feb. 4th: 9 days
Teacher Notes
10-1
Using Models to Compare Fractions: Same Denominator
3.NF.3.d 3.NF.3.a
How can you compare fractions that have the same denominator?
*
10-2
Using Models toCompare Fractions: Same Numerator
3.NF.3.d 3.NF.3.a
How can you compare fractions that have the same numerator?
*
10-3
Comparing Fractions Using Benchmarks
3.NF.3.d
How can benchmark numbers to be used to compare fractions?
*
10-4
Comparing Fractions on the Number Line
How can you compare fractions on a number line?
*
10-5
Finding Equivalent Fractions
How can different fractions name the same number?
*
10-6
Equivalent Fractions and the Number Line
What do equivalent fractions look like on the number line?
*
10-7
Whole Numbers and Fractions
How can whole numbers be described using fraction name?
*
10-8
Using Fractions
10-9
Problem Solving: Draw a Picture
3.NF.3.d 3.NF.3.a 3.NF.3.b 3.NF.3.a
3.NF.3.a 3.NF.3.b 3.NF.3.c 3.NF.3.c
3.NF.3
3.NF.2
Using Fractions
How can you solve a problem by drawing a picture?
HHH Math Grade 3 Curriculum Guide Unit/Topic 12: Time How can lengths of time be measured and found? Why does “what” we measure influence “how” we measure? Why display data in different ways?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
12-1
Time to the Half Hour and Quarter Hour
3.MD.1
How do you tell time to the nearest quarter hour or half hour?
12-2
Time to the Minute
3.MD.1
How do you tell time to the nearest minute?
12-3
Units of Time
3.MD.1
How can you change units of time?
12-4
Elapsed Time
3.MD.1
How can you find elapsed time?
12-5
Problem Solving: Work Backward
3.MD.1
How can you work backwards to solve a problem?
Weeks of March 4th: 6 days
Teacher Notes
**Skip to Unit 15**
HHH Math Grade 3 Curriculum Guide Unit/Topic 15: Liquid Volume and Mass What are the customary units for measuring capacity and weight? What are the metric units for measuring capacity and mass? Why does “what” we measure influence “how” we measure? Why display data in different ways?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of March 12th & 18th: 6 days
15-1
Customary Units of Capacity
3.MD.2
What customary units describe how much a container holds?
15-2
Metric Units of Capacity
3.MD.2
What metric units describe how much a container holds?
15-3
Units of Mass
3.MD.2
What metric units describe mass?
15-4
Units of Weight
3.MD.2
What customary units describe how heavy something is?
15-5
Problem Solving: Draw a Picture
3.MD.2
How can you solve a problem by drawing a picture?
Teacher Notes
HHH Math Grade 3 Curriculum Guide Unit/Topic 16: Data How can data be represented interpreted, and analyzed? Why does “what” we measure influence “how” we measure? Why display data in different ways?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of March 20th & April 1st: 7 days
16-3
Reading Pictographs and Bar Graphs
3.MD.3
How can you read graphs?
16-4
Making a Pictograph
3.MD.3
How do you determine how much a symbol in a pictograph represents?
16-5
Making a Bar Graph
3.MD.3
How can you choose a scale to make a bar graph?
16-6
Problem Solving: Use Tables and Graphs to Draw Conclusions
3.MD.3
What conclusions can you draw from tables and graphs?
Teacher Notes
HHH Math Grade 3 Curriculum Guide Unit/Topic 13: Perimeter How can perimeter be measured and found? Why does “what” we measure influence “how” we measure? Why display data in different ways?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
13-1 & 13-2
Understanding Perimeter Tools and Units for Perimeter
3.MD.8
How do you find the perimeter of a shape? How can you use tools and units to find perimeter?
13-3
Perimeter of Common Shapes
3.MD.8
How can you find the perimeter of common shapes?
13-4
Different Shapes with the Same Perimeter
3.MD.8
What shapes can you make when you know the perimeter?
13-5
Problem Solving: Try Check, and Revise
3.MD.8
How can you use the strategy Try, Check, and Revise to solve problems?
Weeks of April 5th & 8th: 5 days
Teacher Notes
HHH Math Grade 3 Curriculum Guide Unit/Topic 14: Area What does area mean? What are different ways to find the area of a shape? Why does “what” we measure influence “how” we measure? Why display data in different ways? How does geometry better describe objects?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of April 12th, 15th & 22nd: 8 days
14-1
Covering Regions
3.MD.5 3.MD.6
How can you measure area?
14-2
Area and Units
3.MD.5.a 3.MD.5.b
What types of units describe area?
14-3
Standard Units
14-4
Area of Squares and Rectangles
3.MD.7.a 3.MD.7.b
How can you measure the amount of space a figure covers?
14-5
Area and the Distributive Property
3.MD.7.c
How can you break apart rectangles to represent the Distributive Property?
14-7
Area of Irregular Shapes
14-8
Same Area, Different Perimeter
14-9
Equal Areas and Fractions
14-6 & 14-10
Solve a Simpler Problem& Selecting Appropriate Measurement Units and Tools
3.MD.6
3.MD.7.d 3.MD.7.b 3.MD.8
3.G.2 3.MD.2 3.MD.5.a 3.MD.5 3.MD.6 3.MD.7
Teacher Notes
How can you measure area using standard units?
How can you find the area of an irregular figure?
How can rectangles with the same area have different perimeter?
How can you use equal areas to model unit fractions?
How can you use simpler problems to solve a problem? How can you select appropriate measurement units and tools?
Skip to lesson 14-7
Post Assessment Units of Instruction HHH Math Grade 3 Curriculum Guide Unit/Topic 11: Two – Dimensional Shapes and Their Attributes How can two-dimensional shapes be described, analyzed, and classified? How does geometry better describe objects?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Weeks of April 29th & May 6th: 7 days
11-1
Lines and Line Segments
3.G.1
How can you identify points and lines using a number line?
11-2
Angles
3.G.1
How can you describe angles?
11-3
Polygons
3.G.1
What is a polygon?
11-4
Triangles
3.G.1
How can you describe triangles?
11-5
Quadrilaterals
3.G.1
How can you describe quadrilaterals?
Teacher Notes
HHH Math Grade 3 Curriculum Guide Unit/Topic 16: Data How can data be represented interpreted, and analyzed? Why does “what” we measure influence “how” we measure? Why display data in different ways?
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
16-1
Line Plots
3.MD.4
How do you make and use line plots?
16-2
Length and Line Plots
3.MD.4
How can you make line plots to organize and represent data you have collected?
Week of May 5th: 3 days
Teacher Notes
HHH Math Grade 3 Curriculum Guide Unit/Topic 17: Grade Level Priorities Lessons
Common Core State Standard(s)
9-5, 9-6
3.NF.2.a
9-5, 9-7
3.NF.2.b
10-1,10-2,10-4,10-5, 10-6
3.NF.3.a
10-5, 10-6
3.NF.3.b
10-6, 10-7
3.NF.3.c
10-1, 10-2, 10-3, 10-4,
3.NF.3.d
4-1, 4-2, 4-3, 4-4, 4-5
3.OA.1
7-1, 7-2
3.OA.2
All throughout topics 4, 5, 6, 7, 8
3.OA.3
7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 81, 8-2, 8-5, 8-6, 8-7, 8-8
3.OA.4
4-1, 4-2, 4-3, 4-4, 4-5, 6-1, 62, 6-3, 6-4, 6-5, 6-6, 8-7
3.OA.5
5-2, 8-1, 8-2, 8-3, 8-4, 8-8
3.OA.7
2-7, 2-9, 3-3, 3-5, 3-7, 3-8, 310, 5-2, 5-3, 5-4, 5-5, 5-7, 67, 6-9, 8-5
3.OA.8
Remaining weeks of school Essential Understanding(s)
Fractions and decimals allow for quantities to be expressed with greater precision than with just whole numbers.
Fractions can be represented in different formats.
Expressing and comparing quantities and number relationships in different ways helps to demonstrate the value of these amounts.
Mathematical operations are used in solving problems in which a new value found from other values.
It is valuable to understand the relationship between multiplication and division to accurately work with each operation.
Algebraic thinking involves choosing, combining and applying effective strategies for answering problems.
Fluently multiply and divide within 100.
Teacher Notes