Math Curriculum Guide th
4 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 4 Curriculum Guide Unit/Topic 1: Multiplication and Division: Meanings and Fact How can patterns and propertices be used to find some multiplication facts? How can unknown multiplication facts be found by breaking them into known facts? How can unknown division facts be found by thinking about a related multiplication facts? Weeks of Sept. 6, 10, 17th 9 Days Lesson Number and Title 1-1
Meanings of Multiplication
1-2
Patterns for Facts
Common Core State Standard(s) 4.OA.1 4.OA.2 4.OA.5
4.OA.1
Essential Question(s) How can we use arrays to understand multiplication?
Teacher Notes *
What patterns can help you remember multiplication facts for 2s and 5s?
to be combined with 1-4
What happens when you multiply two numbers and switch the order of the factors? What happens when you multiply by zero? If you multiply by one?
* to be combined with lesson 1-8
1-3
Multiplication Properties
1-4
3,4, 6, 7, 8 as Factors
4.OA.4
How can you break apart facts?
1-5
Problem Solving – Look for a Pattern
4.OA.3 4.OA.5
How can a pattern help you solve a problem?
*
1-6
Meanings of Division
4.OA.2
How can you use counters to show that division can be thought of as repeated subtraction or sharing equally?
*
1-7
Relating Multiplication and Division
4.OA.1
How are multiplication and division related?
*
1-8
Special Quotients
4.OA.3
How does the inverse relationship of multiplication and division show why certain division calculations involving 1 make sense?
* to be combined with lesson 1-3
4.OA.3
How can the inverse relationship between multiplication and division by used to find division facts?
*
4.OA.2 4.OA.3
How can a bar diagram help you solve a problem?
*
1-9
1-10
Using Multiplication Facts to Find Division Facts Problem Solving: Draw a Picture and Write an Equation
* to be combined with 1-2
HHH Math 4 Curriculum Guide Unit/Topic 2: How can patterns be used to describe how two quantities are related? How can a relationship between two quantities be shown using a table? Weeks of September 21 and 24th 5 Days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
2-1
Repeating Patterns
4.OA.5
How can you continue a pattern?
2-2
Number Sequences
4.OA.5
What is a pattern?
2-3
Extending Tables
4.OA.5
What pairs of numbers fit a pattern?
2-4
Writing Rules for Situations
4.OA.5
What is a math rule for the situation?
2-5
Geometric Patters
4.OA.5
How can you describe block towers?
2-6
Problem Solving: Act it Out and Use Reasoning
4.OA.3 4.OA.5
How can you solve problems by acting them out and using reasoning?
Topic 2 Test Assessing Lessons 2-2, 2-3, 2-4, and 2-6. Use Test Generator to produce assessment.
Teacher Notes
HHH Math 4 Curriculum Guide Unit/Topic 3: Place Value How are greater numbers read and written? How can whole numbers be compared and ordered? Weeks of October 1 and 8th 9 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
3-1
Representing Numbers
4.NBT.2 4.NBT.1
What are some ways to represent numbers in the thousands?
*
3-2
Place Value Relationships
4.NBT.1 4.NBT.2
How do the digits in a multi-digit number relate to each other?
*
3-3
Comparing Numbers
4.NBT.2
How can place value help you compare numbers?
*
3-4
Ordering Numbers
4.NBT.2
How do you compare numbers?
*
3-5
Rounding Whole Numbers
4.NBT.3
How can you round numbers?
*
3-6
Problem Solving: Make an Organized List
4.NBT.1
How can you use a list to find possible combinations?
*
HHH Math ____ Curriculum Guide Unit/Topic 4: Addition and Subtraction of Whole Numbers How can sums and differences of whole numbers be estimated? What are standard procedures for adding and subtracting whole numbers? Weeks of October 8 and 15th, 8 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
4-1
Using Mental Math to Add and Subtract
4.NBT.3 4.OA.3
How can you use mental math to add and subtract?
*
4-2
Estimating Sums and Differences of Whole Numbers
4.NBT.3 4.NBT.4 4.OA.3
How can you estimate sums and differences of whole numbers?
*
4-3
Adding Whole Numbers
4.NBT.4
How do you add whole numbers?
*
4-4
Subtracting Whole Numbers
4.NBT.4
How do you subtract whole numbers?
*
4-5
Subtracting Across Zeroes
4.NBT.4
How do you subtract across zeroes?
*
4-6
Problem Solving: Draw a Picture and Write an Equations
4.NBT.4 4.OA.3
How can a bar diagram help you solve an addition or subtraction problem?
*
HHH Math ____ Curriculum Guide Unit/Topic 5: Number Sense: Multiplying by one-digit numbers How can some products be found mentally? How can products be estimated? Weeks of October 22 and 29, 8 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
5-1
Arrays and Multiplying by 10 and 100
4.NBT.5
How can you use arrays to multiply by 10 and 100?
*
5-2
Multipying by Multiples of 10 and 100
4.NBT.5
What place value patterns can be seen when you multiply 1 digit numbers by multiples of 10 and 100?
*
5-3
Breaking Apart to Multiply
4.NBT.5
How can you break apart arrays to help you multiply with grater numbers?
*
5-4
Using Mental Math to Multiply
4.NBT.3 4.NBT.5 4.OA.3
What are some ways to multiply mentally?
5-5
Using Rounding to Estimate
4.NBT.3 4.NBT.5
How can you use rounding to estimate when you multiply?
*
5-6
Problem Solving: Reasonableness
4.OA,3 4.NBT.3 4.NBT.5
How do you know if your answer is reasonable?
*
* compensation
HHH Math 4 Curriculum Guide Unit/Topic 6: Developing Fluency: Multiplying by 1 Digit Numbers How can arrays be used to find products? What is the standard procedure for multiplying multi-digit numbers? Weeks of November 5 and 12, 7 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
6-1
Arrays and Using an Expanded Algorithm
4.NBT.5
How can you use models to help you record multiplication?
*
6-2
Connecting the Expanded and Standard Algorithms
4.NBT.5 4.OA.3
How can you record multiplication of a 2 digit number by a 1 digit number?
*
6-3
Multiplying 2 digit by 1 digit number
4.NBT.5 4.OA.3
How can you multiply a 2 digit number and check the product for reasonableness?
*
6-4
Multiplying 3- and 4- digit by 1 digit numbers
4.NBT.5
How do you multiply a 3 digit or 4 digit number by a 1 digit number?
*
6-5
Multiplying by 1 digit numbers
4.NBT.5 4.NBT.3 4.OA.3
How can you estimate to check if an answer to a multiplication problem is reasonable?
*
6-6
Problem Solvig: Missing or Extra Information
4.NBT.5 4.OA.3
How can you tell what information is missing to solve a problem?
*
HHH Math ____ Curriculum Guide Unit/Topic 7: Number Sense: Multiplying by 2 Digit Numbers How can grater products be found mentally? How can greater prodcuts be estimated? Weeks of November 12, 19 and 26th, 7 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
7-1
Arrays and Multiplying 2Digit Numbers by Multiples of 10
4.NBT.5
How can arrays help you multiply a 2-digit number by 10?
7-2
Using Mental Math to Multiply 2-digit numbers
4.NBT.5 4.OA.3
How can you multiply by multiples of 10?
7-3
Using Rounding to Estimate
4.NBT.5 4.OA.3
How can you use rounding to estimate products?
1 of 2 strategies for estimating products
7-4
Using Compatible Numbers to Estimate
4.NBT.5 4.NBT.3 4.OA.3
How can you use compatible numbers to estimate products?
1 of 2 strategies for estimating products Teach this lesson before rounding (7-3)
7-5
Problem Solving: MultiStep Problems
4.NBT.5 4.OA.3
What is the hidden question or questions?
HHH Math 4 Curriculum Guide Unit/Topic 8: Developing Fluency: Multiplying by 2-Digit Numbers How can arrays be used to find greater products? What is the standard procedure for multiplying multi-digit numbers? Weeks of November 26 and December 3, 7 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
8-1
Arrays and Multiplying 2-digit Numbers
4.NBT.5
How can arrays help you multiply 2-digit numbers?
8-2
Arrays and Extended Algorithm
4.NBT.5
How can you record multiplication of 2-digit numbers?
8-3
Multiplying 2-digit numbers by Multiples of 10
4.NBT.5
How can you find the product of a 2-digit number and a multiple of 10?
8-4
Multiplying 2-Digit by 2digit numbers
4.NBT.5
How do you multiply 2-digit by 2-digit numbers?
8-5
Problem Solving: TwoQuestion Problems
4.NBT.5 4.OA.3
How do you use the answer from one question to answer a second question?
Teacher Notes
HHH Math 4 Curriculum Guide Unit/Topic 9: Number Sense: Dividing by 1-digit Divisors What are different meanings of division? How can mental math and estimation be used to divide? Weeks of December 10 and 17th, 8 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
9-1
Using Mental Math to Divide
4.NBT.6 4.OA.3
How can you use place value and patterns to help you divide mentally?
*
9-2
Estimating Quotients
4.NBT.6 4.OA.3
When and how do you estimate quotients to solve problems?
*
9-3
Estimating Quotients for Greater Dividends
4.NBT.6 4.OA.3
How do you estimate quotients using place value?
*
9-4
Dividing with Remainders
4.NBT.6
What does it mean when you divide and some are left over?
*
9-5
Multiplication and Division Stories
4.NBT.6 4.NBT.5
How can you decide when to multiply and when to divide to solve a problem?
*
9-6
Problem Solving: Draw a Picture and Write an Equation
4.NBT.6 4.OA.2 4.OA.3
How can a bar diagram help you solve a division problem?
*
HHH Math 4 Curriculum Guide Unit/Topic 10: Developing Fluency: Dividing by 1-Digit Divisors How can repeated subtraction be used to model division? What is the standard procedure for dividing multi-digit numbers? Weeks of January 2, 7 and 14th, 10 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
10-1
Using Objects to Divide: Division as Repeated Subtraction
4.NBT.6
How can repeated subtraction help you divide?
*
10-2
Division as Repeated Subtraction
4.NBT.6
How can recording division as repeated subtraction help you divide?
*
10-3
Using Objects to Divided: Division is Sharing
4.NBT.6 4.NBT.1
How can place value help you divide?
*
10-4
Dividing 2-Digit by 1Digit Numbers
4.NBT.6
What is a common way to record division?
*
10-5
Dividing 3-Digit by 1Digit Numbers
4.NBT.6
How can you divide numbers in the hundreds?
*
10-6
Deciding Where to Start Dividing
4.NBT.6
What do you do when there are not enough hundreds to divide?
*
10-7
Dividing 4-Digit by 1Digit Numbers
4.NBT.6
How can you estimate larger quotients?
*
10-8
Problem Solving: MultiStep Problems
4.OA.3 4.NBT.5
What hidden questions lie within a mult-step problem?
*
HHH Math 4 Curriculum Guide Unit/Topic 11: Fraction Equivalence and Ordering How can the same fractional amount be named using symbols in different ways? How can fractions be compared and ordered? Weeks of January 14, 21, and 28th, 9 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
11-1
Factors
4.OA.5 4.OA.4
How can you use multiplication to find all the factors of a number?
11-2
Prime and Composite Numbers
4.OA.4
How can you sort numbers by their factors?
11-3
Multiples
4.OA.4 4.OA.5
How can you find the multiples of a number?
11-4
Equivalent Fractions
4.NF.1 4.NF.2
How can you find two fractions that name the same part of a whole?
*
11-5
Number Lines and Equivalent Fractions
4.NF.1 4.NF.2
What does it mean for two fractions to be equivalent?
*
11-6
Comparing Fractions
4.NF.2
How can you use benchmark fractions to compare fractions?
*
11-7
Ordering Fractions
4.NF.2
How can you use equivalent fractions to compare and order fractions?
*
11-8
Problem Solving: Writing to Explain
4.NF.1 4.NF.2
How do you write a good math explanation?
*
HHH Math 4 Curriculum Guide Unit/Topic 12: Adding and Subtracting Fractions and Mixed Numbers with Like Denominators What does it mean to add and subtract fractions and mized numbers with like denominators? What is a standard procedure for adding and subtracting fractions and mixed numbers with like denominators? How can fractions and mixed numbers be added and subtracted on a number line? Weeks of January 28 and February 4 and 11th, 13 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
12-1
Modeling Addition of Fractions
4.NF.3 4.NF.3.a
How can you use fraction strips to add fractions?
*
12-2
Adding Fractions with Like Denominators
4.NF.3.a 4.NF.3.d
How can you add fractions with like denominators?
*
12-3
Modeling Subtraction of Fractions
4.NF.3.a 4.NF.3.d
How can you use fraction strips to subtract fractions?
*
12-4
Subtracting Fractions with Like Denominators
4.NF.3.a 4.NF.3.d
How do you subtract fractions with like denominators?
*
12-5
Adding and Subtracting on the Number Line
4.NF.3.a 4.NF.3.d
How can you use a number line to add and subtract fractions?
*
12-6
Improper Fractions and Mixed Numbers
4.NF.3.c 4.NF.3.b
How are mixed numbers and improper fractions related?
*
12-7
Modeling Addition and Subtraction of Mixed Numbers
4.NF.3.b 4.NF.3.c
How do you use models to add mixed numbers?
*
12-8
Adding Mixed Numbers
4.NF.3.b 4.NF.3.c
How can you add mixed numbers?
*
12-9
Subtracting Mixed Numbers
4.NF.3.c
How can you subtract mixed numbers?
*
12-10
Decomposing and Composting Fractions
4.NF.3.b 4.NF.3.d
How can we use addition to represent a fraction in a variety of ways?
*
12-11
Problem Solving: Draw a Picture and Write an Equation
4.NF.3.a
What operation is needed to solve a problem with fractions?
*
HHH Math 4 Curriculum Guide Unit/Topic 13: Extending Fraction Concepts How is decimal numeration realted to whole number numeration? Week of February 25th, 5 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
13-1
Fractions as Multiples of Unit Fractions: Using Models
4.NF.4.a
How can you describe a fraction using a unit fraction?
*
13-2
Multiplying a Fraction by a Whole Number: Using Models
4.NF.4.b 4.NF.4
How can you find the product of a fraction multiplied by a whole number?
*
13-3
Multiplying a Fraction by a Whole Number: Using Symbols
4.NF.4.c 4.NF.4.b 4.NF.4
When do you need to multiply a fraction by a whole number?
*
HHH Math 4 Curriculum Guide Unit/Topic 15: Solving Measurement Problems What do area and perimeter mean and how can each be found? How can line plots and other tools help to solve measurement problems? Week of March 4th and March 11th 7 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
4.MD.3
How can perimeter and area formulas be used to solve problems?
15-1
Solving Perimeter and Area Problems
15-2
Solving Measurement Problems
4.MD.2
How can the relationship between quantities in a measurement problem be represented using a diagram that can help to solve the problem?
15-3
Solving Problems Using Money
4.MD.2
How can change be given by counting up from one amount of money to another?
15-4
Solving Problems Involving Line Plots
4.MD.4
How can you use line plots to solve problems?
15-5
Problem Solving: Solve a Simpler Problem and Make a Table
4.MD.2
How can you solve a simpler problem and make a table?
Teacher Notes
HHH Math 4 Curriculum Guide Unit/Topic 16: Lines, Angles, and Shapes How can lines, angles, and shapes be described, analyzed, and classified? How are angles measured, added, and subtracted? Weeks of March 11th, 17th, 25th and April 1st, 7 days Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
16-1
Points, Lines, and Planes
4.G.1
What are some important geometric names for lines?
16-2
Line Segments, Rays, and Angles
4.G.1
What geometric terms describe types of angles?
16-3
Understanding Angles and Unit Angles
4.MD.5.a 4.MD.5 4.G.1
How do you find the measure of an angle using equivalent fractions?
16-4
Measuring with Unit Angles
16-5
Measuring Angles
16-6
Adding and Subtracting Angle Measures
16-7
Polygons
4.G.2
How do you identify polygons?
16-8
Triangles
4.G.2
How can you classify triangles?
16-9
Quadrilaterals
4.G.2
How can you classify quadrilaterals?
16-10
Line Symmetry
4.G.3
What is a line of symmetry?
16-11
Problem Solving: Make and Test Generalizations
4.G.2 4.OA.5
How can you test generalizations?
4.MD.5.a 4.MD.5 4.G.1 4.MD.5.b 4.MD.5.a 4.G.1 4.MD.5.b 4.MD.6 4.MD.5.a 4.MD.7 4.MD.5.b 4.MD.6
How are angles measured?
How can you draw an angle?
How can you add and subtract to find unknown angle measures?
Teacher Notes
Post Assessment Units of Instruction HHH Math 4 Curriculum Guide Unit/Topic 13: Extending Fraction Concepts How is decimal numeration realted to whole number numeration? How can decimals be compared and ordered? How are fractions and decimals related? Weeks of April 29th, May 6th, 9 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
Teacher Notes
13-4
Fractions and Decimals
4.NF.5 4.NF.6
How can you write a fraction as a decimal?
*
13-5
Fractions and Decimals on the Number Line
4.NF.5 4.NF.6
How can you locate points for decimals on a number line?
*
13-6
Equivalent Fractions and Decimals
4.NF.5 4.NF.6
How can you use equivalent fractions to change a fraction to a decimal?
*
13-7
Decimal Place Value
4.NF.7
What are some ways to represent decimals?
*
13-8
Comparing and Ordering Decimals
4.NF.7
How do you compare decimals?
*
13-9
Using Money to Understand Decimals
4.MD.2 4.NF.7
How are decimals related to money?
13-10
Problem Solving: Draw a Picture
4.MD.1 4.MD.2 4.NF.6
How can you draw a picture to solve a problem?
*
HHH Math 4 Curriculum Guide Unit/Topic 14: Measurement Units and Conversions What are customary and metric units for measuring length, capacity, and weight/mass, and how are they related? Weeks of May 6, 13 and 19, 13 days
Lesson Number and Title
Common Core State Standard(s)
Essential Question(s)
14-1
Using Customary Units of Length
4.MD.1
How do you estimate and measure length?
14-2
Customary Units of Capacity
4.MD.1
How do you measure capacity with customary units?
14-3
Units of Weight
4.MD.1
How do you measure weight?
14-4
Changing Customary Units
4.MD.1
How do you change customary units?
14-5
Problem Solving: Writing to Explain
4.MD.1
How can you write to explain using measurement?
14-6
Using Metric Units of Length
4.MD.1
How do you estimate and measure length using metric units?
14-7
Metric Units of Capacity
4.MD.1 4.MD.2
How do you measure capacity with metric units?
14-8
Units of Mass
4.MD.1 4.MD.2
How do you measure mass?
14-9
Changing Metric Units
4.MD.1
How do you change metric units?
14-10
Units of Time
4.MD.1 4.MD.2
How do you compare units of time?
14-11
Problem Solving: Work Backward
4.MD.1 4.MD.2
How can you work backward to solve a problem?
Topics 14-1, 14-2, 14-3, 14-4, 14-5, 14-10 and 14-11 assessed together Topics 14-6, 14-7, 14-8, and 14-9 assessed together
Teacher Notes
HHH Math 4 Curriculum Guide Unit/Topic 17: Grade Level Priorities Common Core Lesson Number State Standard(s) 4.OA.1 1-1, 1-3, 1-7
Remaining days of school Essential Understanding(s)
Some problems involving joining or separating equal groups can be solved using multiplication. Repeated addition and joining equal groups are two ways to think about multiplication.
1-6, 1-10
4.OA.2
Use variables in algebraic expressions (multiplication/division) in word problems.
1-5, 1-8, 1-9
4.OA.3
Interpreting remainders in division problems.
3-1, 3-2, 3-6
4.NBT.1
Understanding that a digit in the tens place represents ten times the value of that digit.
3-1, 3-2, 3-3, 34
4.NBT.2
Our number system is based on groups of tens.
3-5, 4-1, 4-2, 54, 5-5, 5-6
4.NBT.3
Rounding using place value. Round up to the hundred thousand place.
4-3, 4-4, 4-5, 46
4.NBT.4
Use place value to add and subtract whole numbers.
5-1 – 5-6, 6-1 – 6-6
4.NBT.5
Multiply four digit by two digit numbers and two digit by two digit numbers using arrays and the break apart method.
Chapters 9 and 10
4.NBT.6
Use thousands dividends and 1 digit divisor to find quotients. Use place value, and models to calculate.
11-4 – 11-8
4.NF.1
Equivalent fractions using visual representations.
11-6 – 11-8
4.NF.2
Comparing fractions (find a common denominator) using fraction strips.
12-1 – 12-11
4.NF.3.a-d
13-1 – 13-3
4.NF.4.a-c
13-4 – 13-5
4.NF.5
Adding fractions with 10 and 100 as denominators.
13-6, 13-10
4.NF.6
Turning a decimal into a fraction.
13-7, 13-8
4.NF.7
Comparing decimals to the hundredth. Understand that decimals must be out of the same whole part.
Describing parts of a whole. Adding fractions with common denominators. Adding and subtraction mixed numbers with like denominators. Word problems that involve adding and subtraction with like denominators. Multiplying a fraction by a whole number. Understand a fraction as a multiple of one. Incorporate multiplying fractions by whole numbers into word problems.
Teacher Notes