Fox River Grove School District #3 Mathematics Curriculum

Transcription

1 Fox River Grove School District #3 Mathematics Curriculum August 2014

2 Table of Contents Philosophy Statement 2 District 3 Mathematics Committee 2 Mathematics Curriculum Kindergarten 3 First Grade 10 Second Grade 14 Third Grade 21 Fourth Grade 28 Fifth Grade 35 Sixth Grade 41 Seventh Grade 48 Eighth Grade 54 2

3 Mathematics Philosophy Fox River Grove School District #3 Mathematics Curriculum is based on NCTM Standards and the Illinois Learning Standards. The curriculum will provide the students with the key skills and understanding they will need to be successful in mathematics both in school and in their daily lives. Note: This guide is aligned to the New Illinois Learning Standards. Each teacher has a copy of these standards. Mathematics Curriculum Committee Lora LeGrand Paulette Nichols Marge Tietz Beth Achey Amy Weicheck Jennie Bebber Stephanie Barham Debbie Wagner, Shirley Slater Debbie Wagner Kindergarten 1 st Grade 2 nd Grade 3 rd Grade 4 th Grade 5 th Grade 6 th Grades 7 th Grade 8 th Grade 3

4 Kindergarten Math Curriculum The following materials form the core of this math program: Textbook: My Math, McGraw-Hill 2013 Teacher s Resource Kit Manipulative Kits Technology: Touch Math Innovative Learning Concepts Counting and Cardinality (CC) Chapter 1: Numbers 0 to 5 How do we show how many? Understand the relationship between numbers and quantities when using objects and illustrations to count 1, 2, and 3. Recognize and write the numerals 1, 2, and 3 and represent a number of objects with a written numeral. Understand the relationship between numbers and quantities when using objects and illustrations to count 4 and 5. Recognize and write the numerals 4 and 5 and represent a number of objects with a written numeral. Recognize and write the numeral 0. Use one-to-one correspondence to determine whether groups are equal to each other. Use one-to-one correspondence to identify a group that is greater than another group. Use one-to-one correspondence to identify a group that is less than another group. Use one-to-one correspondence and counting to compare groups and determine which group is greater than, less than, or whether the groups are equal to each other. Identify numbers from 1 to 5 in sequence understanding that each successive number name is referring to an amount that is one larger. Draw a diagram to solve problems. K.CC.3; K.CC.4; K.CC.4a; K.CC.4b; K.CC.4c; K.CC.5; K.CC.6; K.CC.7 4

5 Chapter 2: Numbers to 10 What do numbers tell me? Name, recognize, and count a quantity of 6 and 7 using concrete objects, illustrations and drawings. Name, recognize, and count a quantity of 8 using concrete objects, illustrations, and drawings. Recognize and write the numerals 6, 7, and 8 and represent a number of objects with a written numeral. Name, recognize, and count a quantity of 9 using concrete objects and motions. Name, recognize, and count a quantity of 10 using concrete objects. Recognize and write the numerals 9 and 10 and represent a number of objects with a written numeral. Act it out to solve problems. Use one-to-one correspondence and counting to compare groups and determine which group is greater than, less than, or whether the groups are equal to each other. Use one more to identify a number that is one larger using numbers to 10. Use ordinal numbers to fifth to describe the position of an object. Use ordinal numbers to tenth to describe the position of an object. K.CC.3; K.CC.4; K.CC.4a; K.CC.4b; K.CC.4c; K.CC.5; K.CC.6; K.CC.7 Chapter 3: Numbers Beyond 10 How can I show numbers beyond 10? Name, recognize, count, and write the numerals 11 and 12 using concrete objects and illustrations. Name, recognize, count, and write the numerals 13 and 14 using concrete objects and illustrations. Name, recognize, count, and write the numeral 15 using concrete objects and illustrations. Name, recognize, count, and write the numerals 16 and 17 using concrete objects and illustrations. Name, recognize, count, and write the numerals 18 and 19 using concrete objects and illustrations. Name, recognize, count, and write the numeral 20 using concrete objects and illustrations. 5

6 Draw a diagram to solve problems. Count and recognize numerals to 50. Count by 100 by ones Count by tens to 100. K.CC.1; K.CC.2; K.CC.3; K.CC.4; K.CC.4a; K.CC.4b; K.CC.4c; K.CC.5 Operations and Algebraic Thinking (OA) Chapter 4: Compose and Decompose Numbers to 10 How can we show a number in other ways? Show ways to compose or make 4 and 5 using concrete objects, drawings, and numbers. Show ways to decompose or take apart 4 and 5 using concrete objects, pictures, and numbers. Show ways to compose or make 6 and 7 using concrete objects, drawings, and numbers. Show ways to decompose or take apart 6 and 7 using concrete objects, pictures, and numbers. Act it out to solve problems. Show ways to compose or make 8 and 9 using concrete objects, drawings, and numbers. Show ways to decompose or take apart 8 and 9 using concrete objects, pictures, and numbers. Show ways to compose or make 10 using concrete objects, drawings, and numbers. Show ways to decompose or take apart 10 using concrete objects, pictures, and numbers. K.OA.1; K.OA.3; K.OA.4 Chapter 5: Addition How can I use objects to add? Model addition by putting groups together or adding to groups. 6

7 Use concrete objects to represent and solve addition problems. Use the plus symbol (+) to show addition. Use the equals symbol (=) in addition sentences. Use concrete objects to show how many in all. Write a number sentence to solve problems. Solve addition problems with numbers one to nine that when added together make 10. K.OA.1; K.OA.2; K.OA.4; K.OA.5 Chapter 6: Subtraction How can I use objects to subtract? Model subtraction as taking away from or separating groups of objects. Use concrete objects to solve subtraction problems. Use the minus symbol (-) to show subtraction. Use the (=) symbol in subtraction sentences. Use concrete objects to show how many are left. Write a number sentence to solve subtraction problems. Take apart 10 by subtracting. K.OA.1; K.OA.2; K.OA.3; K.OA.5 Number and Operations in Base Ten (NBT) Chapter 7: Compose and Decompose Numbers 11 to 19 How do we show numbers 11 to 19 in another way? Compose numbers 11 to 15 using concrete objects and drawings to show a group of 10 and some more. Decompose numbers 11 to 15 using concrete objects and drawings to show a group of 10 and some more. Make a table to solve problems. Compose numbers 16 to 19 using concrete objects and drawings to show a group of 10 or more. 7

8 Decompose numbers 16 to 19 using concrete objects and drawings to show a group of 10 and some more. K.NBT.1 Measurement (MD) Chapter 8: Measurement How do I describe and compare objects by length, height, and weight? Use direct comparison to compare the lengths of objects. Use direct comparison to compare the heights of objects. Guess, check, and revise to solve problems. Use direct measurement to compare objects by weight. Describe measureable attributes of single objects. Compare the capacity of two objects to determine holds more and holds less. Make an organized list to solve problems. Use different strategies, such as patterns models, and arrays, to multiply by 11 and 12. Use different strategies such as equal groups, repeated subtraction, and related facts, to divide by 11 and 12. K.MD.1; K.MD.2 Chapter 9: Classify Objects How do I sort objects? Identify objects that are alike and objects that are different. Use logical reasoning to solve problems. Sort objects into groups by size. Sort objects into groups by shape. Sort by counting. K.MD.3 8

9 Geometry (G) Chapter 10: Positions How do I identify positions? Use the words above and below to describe or place an object with respect to another object. Use the words in front of and behind to describe or place an object with respect to another object. Use the words next to and beside to describe or place an object with respect to another object. Act it out to solve problems. K.G.1 Chapter 11: Two-Dimensional Shapes How can I compare shapes? Identify, name, and describe squares and rectangles. Identify, name, and describe circles and triangles. Identify, name, and describe squares, triangles, circles, and rectangles. Identify, name, and describe hexagons. Compare shapes to understand patterns. Describe objects using the names of shapes and their relative position. Put shapes together to form new shapes. Use logical reasoning to solve problems. Identify shapes in objects and use shapes to create new objects. K.G.1; K.G.2; K.G.3; K.G.4; K.G.5; K.G.6 Chapter 12: Three-Dimensional Shapes How do I identify and compare three-dimensional shapes? Identify, name, and describe cubes and spheres. 9

10 Identify, name, and describe cylinders and cones. Analyze and compare solid shapes. Act it out to solve problems. Identify, name, and describe solid shapes in the physical world. K.G.1; K.G.2; K.G.3; K.G.4 10

11 First Grade Math Curriculum The following materials form the core of this math program: Textbook: My Math, McGraw-Hill Publishing 2013 Teacher s Resource Kit Manipulative Kits Technology: McGraw-Hill Fact Dash Number and Operations in Base Ten (NBT) and Operations and Algebraic Thinking (OA): Chapter 1: Addition Concepts How do you add numbers? How to join parts to make a whole. How to join groups using symbols. Use the Zero Property of Addition to find a sum. How to make a sum of 10 with numbers How to understand the meaning of the equals sign to identify if a math statement is true or false. 1.OA.1; 1.OA.3; 1.OA6; 1.OA.7 Chapter 2: Subtraction Concepts How do you subtract numbers? How to take away a part from the whole. How to use addition facts to find subtraction facts. How to use symbols to show take away situations. How to compare groups using subtraction. 1.OA.1; 1.OA.6 Chapter 3: Addition Strategies 11

12 How do I use strategies to add numbers? How to apply properties of operations to add. How to count on to add another number. How to use a number line to add. How to use doubles to add. How to add near doubles to find the sum. 1.OA.3; 1.OA.5; 1.OA.6 Chapter 4: Subtraction Strategies What strategies can I use to subtract? How to count back to subtract. How to take apart a number to subtract to make 10. How to find a missing addend using addition and subtraction. How to use the same four numbers to add and subtract. 1.OA.5; 1.OA.6;1.OA.4; 1.OA.8 Chapter 5: Place Value How can I use place value? Read and write numerals and represent a number of objects with a written numeral. How to make ten using ones. How to show a number as tens and ones. How to compare two-digit numbers using equal to (=), greater than (>), and less than (<). Mentally find ten more and/or ten less than a given number without having to count the numbers. 1.NBT.1; 1.NBT.2a; 1.NBT.3; 1.NBT.5 12

13 Chapter 6: Two-Digit Addition and Subtraction How can I add and subtract two-digit numbers? How to add groups of tens within 100. How to count on by tens or by ones to solve a two-digit addition problem. How to add numbers with regrouping. How to subtract by tens to find the difference. How to use a number line to count back by tens. 1.NBT.4; 1.NBT.6 Measurement (MD) Chapter 7: Organize and Use Graphs How do I make and read graphs? Organize, represent, ad interpret data using a tally chart. Organize and represent data with up to three categories using a picture graph. Organize, represent, and interpret data with up to three categories on a bar graph. 1.MD.4 Chapter 8: Measurement and Time How do I determine length and time? How to compare objects by length. How to express the length of an object as a whole number of length units. How to tell time on an analog clock. How to tell time on a digital clock. 1.MD.1; 1.MD.2; 1.MD.3 13

14 Geometry (G) Chapter 9: Two-Dimensional Shapes and Equal Shares How can I recognize two-dimensional shapes and equal shares? How to recognize two-dimensional shapes by defining attributes. How to make a new shape by putting other shapes together. How to partition shapes into equal parts. 1.G.1; 1.G.2; 1.G.3 Chapter 10: Three-Dimensional Shapes How can I identify three-dimensional shapes? Distinguish between defining attributes and non-defining attributes to identify a cube. Distinguish between defining attributes and non-defining attributes to identify a rectangular prism. Distinguish between defining attributes and non-defining attributes to identify a cylinder. Distinguish between defining attribute and non-defining attribute to identify a cone. How to combine three-dimensional shapes to make a composite shape. 1.G.1; 1.G.2 Additional Money Unit -- Supplemental Materials if time allows Coin identification Coin value Counting coins to sum of $

15 Second Grade Math Curriculum The following materials form the core of this math program: Textbook: My Math, Macmillan McGraw-Hill, 2013 Teacher s Resource Kit Operations and Algebraic Thinking Chapter 1: Apply Addition and Subtraction Concepts What strategies can I use to add and subtract? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Addition Properties Count On to Add Doubles and Near Doubles Make A 10 Add Three Numbers Problem-Solving Strategy: Write a Number Sentence Check My Progress Count Back to Subtract Subtract All and Subtract Zero Use Doubles to Subtract Relate Addition and Subtraction Missing Addends Fact Families Two-Step Word Problems Wrap Up: Fluency Practice; My Review; Reflect 2.OA.1; 2.OA.2; 2.NBT.5; 2.NBT.9; 2.MD.6 Chapter 2: Number Patterns How can equal groups help me add? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable 15

16 Skip Count on a Hundred Chart Skip Count by 2s, 5s, and 10s. Problem-Solving Strategy: Find a Pattern Check My Progress Repeated Addition Repeated Addition with Arrays Even and Odd Numbers Sums of Equal Numbers Wrap Up: Fluency Practice; My Review; Reflect 2.OA.1; 2.OA.2; 2.OA.3; 2.OA.4; 2.NBT.2 Chapter 3: Add Two-Digit Numbers How can I add two-digit numbers? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Take Apart Tens to Add Regroup Ones as Tens Add to a Two-Digit Number Check My Progress Add Two-Digit Numbers Rewrite Two-Digit Addition Add Three or Four Two-Digit Addition Problem-Solving Strategy: Make a Model Wrap Up: Fluency Practice; My Review; Reflect 2.NBT.92.OA.1; 2.NBT.5; 2.NBT.6; Chapter 4: Subtract Two-Digit Numbers How can I subtract two-digit numbers? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Two-Digit Fact Families Take Apart Tens to Subtract Regroup a Ten as Ones 16

17 Subtract From a Two-Digit Number Check My Progress Subtract Two-Digit Numbers Rewrite Two-Digit Subtraction Check Subtraction Problem-solving Strategy: Write a Number Sentence Two-Step Word Problems Wrap Up: Fluency Practice; My Review; Reflect 2.OA.1; 2.NBT.5; 2.NBT.9 Number and Operations in Base Ten Chapter 5: Place Value to 1,000 How can I use place value? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Hundreds Hundreds, Tens, and Ones Place Value to 1,000 Check My Progress Problem-Solving Strategy: Use Logical Reasoning Read and Write Numbers to 1,000 Count by 5s, 10s, and 100s Compare Numbers to 1,000 Wrap up: My Review; Reflect 2.NBT.1; 2.NBT.1a; 2.NBT.1b; 2.NBT.2; 2.NBT.3; 2.NBT.4; 2.NBT.8 Chapter 6: Add Three-Digit Numbers How can I add three-digit numbers? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Make a Hundred to Add 17

18 Add Hundreds Mentally Add 10 or 100 Check My Progress Regroup Ones to Add Regroup Tens to Add Add Three-Digit Numbers Rewrite Three-Digit Addition Problem-solving Strategy: Guess, Check, and Revise Wrap Up: My Review: Reflect 2.NBT.7; 2.NBT.8; 2.NBT.9 Chapter 7: Subtract Three-Digit Numbers How can I subtract three-digit numbers? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Take Apart Hundreds to Subtract Subtract Hundreds Mentally Subtract 10 or 100 Check My Progress Regroup Tens Regroup Hundreds Subtract Three-Digit Numbers Rewrite Three-Digit Subtraction Problem Solving Strategy: Write a Number Sentence Subtract Across Zeros Wrap Up: My Review; Reflect 2.NBT.7; 2.NBT.8; 2.NBT.9 Measurement and Data Chapter 8: Money How do I count and use money? 18

19 Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Pennies, Nickels, and Dimes Quarters Count Coins Check My Progress Problem-Solving Strategy: Make a Model Dollars Wrap Up: My Review; Reflect 2.MD.8 Chapter 9: Data Analysis How can I record and analyze data? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Take a Survey Make Picture Graphs Analyze Picture Graphs Check My Progress Make Bar Graphs Problem-Solving Strategy: Make a Table Make Line Plots Analyze Line Plots Wrap Up: My Review; Reflect 2.MD.9; 2.MD.10 Chapter 10: Time How do I use and tell time? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Time to The Hour Time to the Half Hour 19

20 Problem-Solving Strategy: Find a Pattern Check My Progress Time to the Quarter Hour Time to Five Minute Intervals A.M. and P.M. Wrap Up: My Review; Reflect 2.MD.7 Chapter 11: Customary and Metric Lengths How can I measure objects? Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Inches Feet and Yards Select and Use Customary Tools Check My Rogress Compare Customary Lengths Relate Inches, Feet, and Yards Problem-solving Strategy: Use Logical Reasoning Check My Progress Centimeters and Meters Select and Use Metric Tools Compare Metric Lengths Relate Centimeters and Meters Measure on a Number Line Measurement Data Wrap Up: My Review; Reflect 2.MD.1; 2.MD.2; 2.MD.3; 2.MD.4; 2.MD.5; 2.MD.6 Geometry Chapter 12: Geometric Shapes and Equal Shares How do I use shapes and equal parts? 20

21 Getting Started: Am I Ready?; My Math Words; My Vocabulary Cards; My Foldable Two-Dimensional Shapes Sides and Angles Problem-Solving Strategy: Draw a Diagram Check My Progress Three- Dimensional Shapes Faces, Edges, and Vertices Relate Shapes and Solids Halves, Thirds, and Fourths Area Wrap Up: My Review; Reflect 2.G.1; 2.G.2; 2.G.3 21

22 Third Grade Math Curriculum The following materials form the core of this math program: Textbook: My Math, McGraw-Hill Publishing 2013 Teacher s Resource Kit Manipulative Kits Technology: for home and school fact practice Math CD-ROM lab packs for use in classroom Number and Operations in Base Ten (NBT) and Operations and Algebraic Thinking (OA): Chapter 1: Place Value How can numbers be expressed, ordered, and compared? Read, write, and identify place value of whole numbers through thousands. Use place value to compare numbers. Use number line and place value to order numbers through thousands. Round numbers to the nearest ten. Round numbers to the nearest hundred. Use the four-step plan to solve problems. 3.NBT.1; 3.NBT.2; 3.NBT.3; Chapter 2: Addition How can place value help me add larger numbers? Use addition properties to add whole numbers. Identify patterns in the addition table. Use place value to identify addition patterns. Use mental addition strategies. Estimate sums using rounding. Use models to explore adding three-digit numbers. Add three-digit numbers and use estimation to check for reasonableness. Add four-digit numbers with regrouping. Check answers for reasonableness. 22

23 3.NBT.2; 3.OA.9 Chapter 3: Subtraction How are the operations of addition and subtraction related? Use strategies to subtract mentally. Estimate differences using rounding to the nearest ten or hundred. Determine whether an estimate or exact answer is needed to solve a problem. Model subtraction with regrouping. Subtract three-digit numbers with regrouping. Subtract four-digit numbers with regrouping. Subtract across zeros. 3.NBT.2; 3.OA.8 Chapter 4: Understand Multiplication What does multiplication mean? Use models to explore the meaning of multiplication. Relate multiplication and addition. (Repeated addition) Use arrays to explore and model multiplication. Use arrays to multiply. Use the make a table strategy to solve problems. Use multiplication to find the total number of combinations that can be made when given two groups of objects. 3.OA.1; 3.OA.3; 3.OA.5; 3.OA.8 Chapter 5: Understand Division What does division mean? Explore two meanings of division. 23

24 Model division as equal sharing. Use models to relate division and subtraction. Explore how division and multiplication are related. Divide using related multiplication facts. (Inverse operations) Use models to solve problems. 3.OA.2; 3.OA.4; 3.OA.6; 3.OA.7 Chapter 6: Multiplication and Division Patterns What is the importance of patterns in learning multiplication and division? Identify and explain patterns in the multiplication table. Use arrays and drawings, such as bar diagrams, to multiply by 2. Use models and related multiplication facts to divide by 2. Use different strategies, including patterns, to multiply by 5. Use different strategies, including related multiplication facts, to divide by 5. Solve problems by looking for a pattern. Use different strategies, including patterns, to multiply by 10. Use basic facts and patterns to multiply a number by a multiple of 10. Use different strategies, including related multiplication facts, to divide by OA.1; 3.OA.2; 3.OA.3; 3.OA.4; 3.OA.5; 3.OA.6; 3.OA.7; 3.OA.9 Chapter 7: Multiplication and Division What strategies can be used to learn multiplication and division facts? Use different strategies, such as arrays, equal groups, and properties, to multiply by 3. Use different strategies, including related multiplication facts, to divide by 3. Explore how to double a known fact in order to multiply. Double a known fact to multiply by 4. Use different strategies, including related multiplication facts, to divide by 4. Solve a problem by identifying extra or missing information. Use different strategies, such as equal groups, patterns, and properties, to multiply by 0 and 1. Use division rules to divide with 0 and 1. 24

25 3.OA.1; 3.OA.2; 3.OA.3; 3.OA.4; 3.OA.5; 3.OA.6; 3.OA.7; 3.OA.9 Chapter 8: Apply Multiplication and Division How can multiplication and division facts with smaller numbers be applied to larger numbers? Use different strategies, including doubling a know fact, to multiply by 6. Use different strategies, such as properties, arrays, and decomposing factors, to multiply by 7. Use different strategies, including arrays, and repeated subtraction, to divide by 6 and 7. Use different strategies, such as arrays, drawings, and known facts, to multiply by 8. Use different strategies, such as properties, know facts, or patterns, to multiply by 9. Use different strategies, such as equal groups, repeated subtraction, and related multiplication facts, to divide by 8 and 9. Make an organized list to solve problems. Use different strategies, such as patterns models, and arrays, to multiply by 11 and 12. Use different strategies such as equal groups, repeated subtraction, and related facts, to divide by 11 and OA.1; 3.OA.2; 3.OA.3; 3.OA.4; 3.OA.5; 3.OA.6; 3.OA.7; 3.OA. 9 Chapter 9: Properties and Equations How are properties and equations used to group numbers? Explore how to take apart factors to multiply. Apply the Distributive Property to find products. Explore how to find the product of three factors. Apply the Associative Property of Multiplication to find products. Write expressions using the four operations. Evaluate expressions. Write, and then find the value of expressions. Write equations: Represent one- and two-step word problems using equations with a variable. 25

26 Represent and solve two-step word problems using equations with a variable. Use logical reasoning to solve problems. 3.OA.5; 3.OA.7; 3.OA.8 Numbers and Operations: Fractions (NF) and Geometry (G) Chapter 10: Fractions How can fractions be used to represent numbers and their parts? Explore and model unit fractions. Read and write fractions that are part of a whole. Use models to represent fractions that name part of a set. Draw a diagram to solve problems. Represent fractions on a number line. Use models to find equivalent fractions. Express whole numbers as fractions and recognize fractions equivalent to whole numbers. Use models to compare two fractions and record the results. 3.NF.1; 3.NF.2; 3.NF.2a; 3.NF.2b; 3.NF.3; 3.NF.3a; 3.NF.3b; 3.NF.3c; 3.NF.3d; 3.G.2 Measurement (MD) Chapter 11: Measurement Why do we measure? Explore estimating and measuring liquid volume using metric units of capacity. Use the four operations to solve one-step word problems involving liquid volume. Explore estimating and measuring metric units of mass. Use the four operations to solve one-step word problems involving mass. Tell time to the nearest minute. 26

27 Determine time intervals to solve problems. Work backward to solve problems. 3.MD.1; 3.MD.2; 3.OA.3 Chapter 12: Represent and Interpret Data How do we obtain information from a set of data? Collect and record data through observations and surveys. Draw a scaled picture graph. Draw scaled bar graphs. Relate bar graphs to scaled picture graphs. Draw, organize, and analyze data in line plots. Measure lengths to the nearest half inch and nearest quarter inch. Collect and display measurement data to fractions of an inch. Solve problems by solving a simpler problem. 3.MD.3; 3.MD.4 Chapter 13: Perimeter and Area How are perimeter and area related and how are they different? Explore finding the perimeter of a figure. Find the unknown when solving problems involving perimeter. Count unit squares to find the area of a figure. Use addition to measure the area of a figure. Use tiling to find the area of rectangles. Use the formula for area to find the area of rectangles. Use the Distributive Property to find area. Find the area of composite figures. Recognize the relationship between area and perimeter. Draw a diagram to solve problems. 3.MD.5; 3.MD.5a; 3.MD.5b; 3.MD.6; 3.MD.7; 3.MD.7a; 3.MD.7b; 3.MD.7c; 3.MD.7d; 3.MD.8 27

28 Geometry (G) Chapter 14: Geometry How can geometric shapes help me solve real world problems? Explore angles of two-dimensional figures. Describe and classify polygons by their attributes. Describe and classify triangles by their attributes. Identify, describe, and classify quadrilaterals by their attributes. Describe the shared attributes of quadrilaterals. Use the guess, check, and revise strategy to solve problems. Partition shapes into equal sections and write unit fractions to represent each area. 3.G.1; 3.G.2 28

29 Fourth Grade Math Curriculum The following materials form the core of this math program: Textbook: My Math, McGraw-Hill Publishing 2013 Teacher s Resource Kit Manipulative Kits Technology: Number and Operations in Base Ten (NBT) (OA) : Chapter 1: Place Value How does place value help represent the value of numbers? Identify the place value of digits in multi-digit numbers. Read and write multi-digit whole numbers. Compare numbers using a number line and place value chart. Order numbers by using a place-value chart and comparing the digit values. Estimate numbers by rounding. Use the four-step plan to solve problems. 4.NBT.1; 4.NBT.2; 4.NBT.3 Chapter 2: Add and Subtract Whole numbers What strategies can I use to add and subtract? Use addition properties and subtraction rules to add and subtract. Use patterns to solve addition and subtraction problems. Use place value to identify addition patterns. Use mental math to add and subtract. Estimate sums and differences of multi-digit numbers. Add multi-digit whole numbers. Subtract multi-digit whole numbers. Subtract multi-digit whole numbers when some digits are zeros. Solve problems by drawing a diagram. Solve multi-step word problems using addition and subtraction. 4.NBT.3; 4.NBT.4;4.OA.3; 4.OA.5 29

30 Chapter 3: Understand Multiplication and Division How are multiplication and division related? Understand how multiplication and division are related.. Relate division and subtraction. Recognize the comparison of two groups as another strategy to use when multiplying. Use comparison to solve problems. Use multiplication properties and division rules. Use the Associative Property of Multiplication to solve problems. Find factors and multiples of whole numbers. Check for reasonableness. 4.NBT.5; 4.NBT.6; 4.OA.1; 4.OA.2; 4.OA.4 Chapter 4: Multiply with One-digit Numbers How can I communicate multiplication? Multiply multiplies of 10, 100, and 1,000 using basic facts and patterns. Estimate products by rounding. Explore multiplication using models. Explore multiplication using area models and partial products. Multiply a two-digit number by a one-digit number. Explore multiplication with regrouping using models. Use the distributive Property to make multiplication easier. Multiply a two-digit number by a one-digit number. Multiply a multi-digit number by a one-digit number. Determine if a problem needs an estimate or an exact answer. Multiply multi-digit numbers with zeros by a one-digit number. 4.NBT.1; 4.NBT.3; 4.NBT.5; 4.OA.3; 4.OA.4 Chapter 5: Multiply with Two-Digit Numbers How can I multiply by a two-digit number? 30

31 Use properties and algorithms to multiply by tens. Estimate products by rounding. Explore multiplying by two-digit numbers. Multiply two, two-digit numbers. Use multiplication to solve multi-step word problems. Solve problems by making a table. 4.NBT.3; 4.NBT.4; 4.NBT.5; 4.OA.3 Chapter 6: Divide By a One-Digit Number How does division effect numbers? Use basic facts and patterns to divide mentally. Estimate quotients, using compatible numbers, basic facts, and place value. Use place value and models to explore dividing by one-digit numbers. Solve problems by making a model. Divide with remainders and check using multiplication and addition. Interpret what the remainder means in the context of a division problem. Determine where to place the first digit when dividing. Use the Distributive Property and partial quotients to divide. Solve problems with greater numbers. Solve division problems that result in quotients that have zeros. Solve multi-step word problems using more than one operation. 4.NBT.1; 4.NBT.3; 4.NBT.6; 4.OA.3; 4.OA.4 Operations and Algebraic Thinking (OA): Chapter 7: Patterns and Sequences How are patterns used in mathematics? Describe nonnumeric growing and repeating patterns. Identify, describe, and extend numeric patterns. Extend patterns and write observations about the pattern. Look for a pattern to solve problems. Find and use rules to write addition and subtraction equations. Find and use rules to write multiplication and division equations. 31

32 Use the order of operations to solve problems. Explore equations with two operations. Use tables to recognize and write equations with two operations. 4.OA.3; 4.OA.5 Number and Operations-Fractions Chapter 8: Fractions How can different fractions name the same amount? Find factors and multiples of whole numbers. Determine if a number is prime or composite. Explore equivalent fractions. Write a fraction in simplest form. Compare and order fractions. Use benchmark fractions to compare and order numbers. Use logical reasoning to solve problems. Represent mixed numbers by decomposing them into a sum of whole numbers and unit fractions. Write mixed numbers and improper fractions. 4.NF.1; 4.NF.2; 4.NF.3; 4.NF.5; 4.OA.4 Chapter 9: Operations with Fractions How can I use operations to model real-world fractions? Use models to add like fractions. Add like fractions. Use models to subtract like fractions. Subtract like fractions. Work backward to solve problems. Add mixed numbers Subtract mixed numbers Use models to multiply fractions. Multiply fractions by whole numbers. 32

33 4.NF3; 4.NF.4 Chapter 10: Fractions and Decimals How are fractions and decimals related? Explore using place-value charts and grids to model decimals. Model and describe tenths as part of the base-ten system. Model and describe hundredths as part of the base-ten system. Explore using grids and number lines to model the relationship between decimals and fractions. Identify, read, and write tenths and hundredths as decimals and as fractions. Use place value and equivalent fractions to add two fractions with respective denominators 10 and 100. Compare and order decimals to hundredths by reasoning about their size. Find extra or missing information when solving problems. 4.NF.5; 4.NF.6; 4.NF.7 Measurement and Data (MD) Chapter 11: Customary Measurement Why do we convert measurements? Estimate and measure length using customary units. Convert units of length. Estimate and measure customary capacities. Convert customary units of capacity. Estimate and measure customary units of weight. Convert customary units of weight. Convert units of time. Display measurement data in a line plot. Solve problems involving measurement. Solve problems using the guess, check, and revise strategy. 4.MD.1; 4.MD.2; 4.MD.4 33

34 Chapter 12: Metric Measurement How can conversions of measurements help me solve real-world problems? Estimate and measure lengths within the metric system. Estimate and measure metric capacities Estimate and measure mass and learn the difference between weight and mass. Make an organized list to solve problems. Convert metric units. Solve problems involving measurement. 4.MD.1; 4.MD.2 Chapter 13: Perimeter and Area Why is it important to measure area and perimeter? Find the perimeter of a figure. Solve a simpler problem to solve problems. Explore the area of a figure. Find the area of rectangles and squares. Relate area to perimeter. 4.MD.3 Geometry (G) Chapter 14: Geometry How are different ideas about geometry connected? Draw points, lines, line segments, and rats and identify these in twodimensional figures. Draw parallel, interacting, and perpendicular lines, and identify these in twodimensional figures. Understand concepts of angles and angle measurement. Use concepts of angle measurement to classify angles. 34

35 Use a protractor to measure angles to the nearest degree. Use a protractor to draw angles of a specified measure. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical situations. Classify triangles based on angle measure and describe triangles using their attributes. Classify quadrilaterals using their attributes. Identify figures with line symmetry and draw lines of symmetry. Solve problems by making a model. 4.G.1; 4.G.2; 4.G.3; 4.MD.5; 4.MD.6; 4.MD.7 35

36 Fifth Grade Math Curriculum The following materials form the core of this math program: Textbook: My Math, McGraw-Hill Publishing 2013 Web-sites: o o : Used as practice and remediation. IPads: various apps for practice and remediation Number and Operations in Base Ten (NBT): Chapter 1: Place Value How does the position of a digit in a number relate to its value? Place value through millions Compare and order whole numbers through millions Represent decimals Place value through thousandths Compare decimals Order whole numbers and decimals 5.NBT.1; 5.NBT.3; 5.NBT.3a; 5.NBT.3b Chapter 2: Multiply Whole Numbers Essential Questions: What is multiplication? What strategies can be used to multiply whole numbers? In what ways can operations affect numbers? Prime factorization Powers and exponents Multiplication patterns Distributive property Estimate products Multiply by one-digit numbers Multiply by two-digit numbers 5.NBT.2; 5.NBT.5 36

37 Chapter 3: Divide by a One-Digit Divisor Essential Questions: What is division? What strategies can be used to divide whole numbers? In what ways can operations affect numbers? Relate division to multiplication Two-digit dividends Division patterns Estimate quotients Distributive property and partial quotients Divide three- and four-digit dividends Place the first digit Quotients with zeroes Interpret the remainder 5.NBT.6 Chapter 4 : Divide by a Two-Digit Divisor What strategies can I use to divide by a two-digit divisor? Estimate quotients Divide by a two-digit divisor Adjust quotients Divide greater numbers 5.NBT.6 Chapter 5: Add and Subtract Decimals Essential Questions: How can I use place value and properties to add and subtract decimals? How can different strategies be helpful when solving a problem? Round decimals Estimate sums and differences Add decimals 37

38 Addition properties o Commutative o Associative o Identity Subtract decimals 5.NBT.4; 5.NBT.7 Chapter 6: Multiply and Divide Decimals Essential Questions: How is multiplying and dividing decimals similar to multiplying and dividing whole numbers? How does the position of a digit in a number relate to its value? Estimate products of whole numbers and decimals Multiply decimals by whole numbers Multiply decimals Multiply decimals by powers of ten Multiplication properties o Associative o Commutative o Identity Estimate quotients Divide decimals by whole numbers Divide decimals Divide decimals by powers of ten 5.NBT.2; 5.NBT.4; 5.NBT.5; 5.NBT.7 Operations and Algebraic Thinking (OA): Chapter 7: Expressions and Patterns Essential Questions: How are patterns used to solve problems? How can different strategies be helpful when solving a problem? Order of operations Write numerical expressions Patterns Map Locations 38

39 Ordered pairs Graph patterns 5.OA.1; 5.OA.2; 5.OA.3; 5.G.1; 5.G.2 Number and Operations Fractions (NF): Chapter 8: Fractions and Decimals How are factors and multiples helpful in solving problems? Fractions and division Greatest common factor Simplest form Least common multiple Compare fractions Write fractions as decimals 5.NF.2; 5.NF.3; 5.NF.5; 5.NF.5b Chapter 9: Add and Subtract Fractions How can equivalent fractions help me add and subtract fractions? Round fractions Add like fractions Subtract like fractions Add unlike fractions Subtract unlike fractions Determine reasonable answers Add mixed numbers Subtract mixed numbers 5.NF.1; 5.NF.2; Chapter 10: Multiply and Divide Fractions What strategies can be used to multiply and divide fractions? 39

40 Part of a number Estimate products of fractions Fraction multiplication Multiply whole numbers and fractions Use models to multiply fractions Multiply fractions Multiply mixed numbers Multiplication of scaling Division with unit fractions Divide whole numbers by unit fractions Divided unit fractions by whole numbers Draw a diagram 5.NF.4; 5.NF.4a; 5.NF.4b;5.NF.5; 5.NF.5a; 5.NF.5b; 5.NF.6; 5.NF.7; 5.NF.7a; 5.NF.7b;5.NF.7c Measurement and Data (MD): Chapter 11: Measurement Essential Questions: How can I use measurement conversions to solve real-world problems? Why express quantities and measurements in different ways? Why does what we measure influence how we measure? Why display data in different ways? Measure with a ruler Convert customary units of length Use logical reasoning Estimate and measure weight Convert customary units of weight Estimate and measure capacity Convert customary units of capacity Display measurement data on a line plot Use metric rulers Convert metric units of length Estimate and measure metric mass Convert metric units of mass Convert metric units of capacity 5.MD.1; 5.MD.2 40

41 Geometry (G): Chapter 12: Geometry Essential Questions: How does geometry help me solve problems in everyday life? How does geometry better describe objects? Polygons Sides and angles of triangles Classify triangles Sides and angles of quadrilaterals Classify quadrilaterals Build three-dimensional figures Three-dimensional figures Use models to find volume Volume of prisms Build composite figures Volume of composite figures Make a model 5.G.3; 5.G.4; 5.MD.3; 5.MD.3a; 5.MD.3b; 5.MD.4; 5.MD. 5; 5.MD.5a; 5.MD.5b; 5.MD.5c 41

42 6 th Grade Math Curriculum The following materials form the core of this math program: McDougal Littell Middle School Math Course 1 Teacher s Resource Package: o Chapter Resource Books (one for each chapter, organized by lesson) o Assessment Book o Note Taking Guide Teacher s Edition o Practice Workbook Teacher s Edition o Teacher Survival Kit (includes the Professional Development Book, the Special Activities Book, and the Poster Package) o Warm-Up Transparencies with Daily Homework Quiz o Worked-Out Solution Key Technology: provides instruction, practice, and learning support Chapter 1: Number Sense and Algebraic Thinking Chapter Overview: In this chapter, students compute and estimate with whole numbers. They evaluate powers and use the order of operations to evaluate expressions, including expressions that contain variables. Students also solve equations using mental math and learn a problem-solving plan. add, subtract, multiply, and divide whole numbers round to estimate with whole numbers find values of powers evaluate expressions using the order of operations evaluate expressions that involve variables solve equations using mental math use a 4-step plan to solve many kinds of problems [State Standard/IMAF: ; ; ; ; ; 6.617; ; ; ] Chapter 2: Measurement and Statistics Chapter Overview: In this chapter, students measure lengths and find the perimeter and area of geometric figures. They also find actual lengths from scale drawings. They create and interpret frequency tables, line plots, and display data in bar graphs. They plot points in the first quadrant to make line graphs. Students also interpret circle graphs, and describe data using mean, median, mode, and range. 42

43 measure length using customary and metric units use formulas to find perimeter and area use scale drawings to find actual lengths create and interpret frequency tables and line plots display data using bar graphs plot points on coordinate grids and make line graphs interpret circle graphs and make predictions describe data using mean, median, mode, and range [State Standard/IMAF: ; ; ; ; ; ; ; ; ; ] Chapter 3: Decimal Addition and Subtraction Chapter Overview: In this chapter, students explore decimals. They begin with place values to hundred-thousandths, and they model decimals using money and metric lengths. Then they order decimals using a number line and round decimals. Finally, they find the sum or difference of two decimals or of a decimal and a whole number. read and write decimals use decimals to express metric measurements compare and order decimals round decimals estimate sums and differences of decimals add and subtract decimals [State Standard/IMAF: ; ; ; ; ; ; ; ; ] Chapter 4: Decimal Multiplication and Division Chapter Overview: In this chapter, students continue to investigate decimals. They start by using the distributive property and area models to develop skill in multiplying with decimals. They explore multiplying and dividing by powers of 10 and then explore dividing decimals by whole numbers or by other decimals. Students also use metric measurements for mass, capacity, and length. 43

44 multiply decimals and whole numbers use the distributive property to evaluate expressions multiply decimals by decimals divide decimals by whole numbers use mental math to help multiply and divide divide by decimals use metric units of mass and capacity change from one metric unit of measure to another [State Standard/IMAF: ; ; ; ; ; ; ] Chapter 5: Number Patterns and Fractions Chapter Overview: In this chapter, students investigate prime factorization and fractions. They relate prime factorization to the greatest common factor and to the least common multiple of pairs of numbers. With fractions, students use area models to find equivalent fractions, and then they order fractions. Students also convert between mixed numbers and improper fractions, and rewrite decimals as fractions or mixed numbers. Finally, they rewrite fractions as decimals and explore repeating decimals. write whole numbers as the product of prime factors find the greatest common factor of two or more numbers write equivalent fractions find least common multiples compare and order fractions rewrite mixed numbers and improper fractions write a decimal as a fraction write fractions as decimals [State Standard/IMAF: ; ; ; ; ] Chapter 6: Addition and Subtraction of Fractions Chapter Overview: In this chapter, students estimate sums and differences of fractions and mixed numbers. They also add and subtract fractions and mixed numbers. Finally, students will add and subtract measures of time. 44

45 estimate with fractions and mixed numbers find actual sums and differences of fractions add and subtract with different denominators add and subtract mixed numbers subtract mixed numbers by renaming add and subtract measures of time [State Standard/IMAF: ; ; ] Chapter 7: Multiplication and Division of Fractions Chapter Overview: In this chapter, students multiply and divide with fractions and mixed numbers. The concepts are introduced by using an area model for multiplying fractions and a ruler model for dividing fractions. Students also explore customary units for weight, capacity, and length, including changing units of measure. multiply fractions and whole numbers multiply fractions multiply mixed numbers use reciprocals to divide fractions divide mixed numbers use customary units of weight and capacity change customary units of measure [State Standard/IMAF: ; ; ; ] Chapter 8: Ratio, Proportion, and Percent Chapter Overview: In this chapter, students study ratios, rates, proportions, and percents. They simplify and find equivalent ratios and rates, and they calculate and use unit rates. They solve proportions formed by pairs of equal ratios or rates, and they apply proportions to work with scale drawings. Students also investigate percent. They write fractions and decimals as percents, they use percents in circle graphs, and they find a percent of a number in problems involving discounts, tax, and simple interest. write ratios and equivalent ratios 45

46 write rates, equivalent rates, and unit rates write and solve proportions use proportions to find measures of objects write percents as decimals and fractions write fractions and decimals as percents multiply to find a percent of a number [State Standard/IMAF: ; ; ; ; ; ] Chapter 9: Geometric Figures Chapter Overview: In this chapter, students study segments, lines, planes, and angles. They name and classify triangles by their sides or angles, and they classify quadrilaterals by their angles and sides. Students identify similar and congruent figures, and they find lines of symmetry. identify lines, rays, and segments name, measure, and draw angles classify angles and find angle measures classify triangles by their angles and by their sides classify quadrilaterals by their angles and sides classify polygons by their sides identify similar and congruent figures identify lines of symmetry [State Standard/IMAF: ; ; ; ; ; ; ] Chapter 10: Geometry and Measurement Chapter Overview: In this chapter, students find the area of parallelograms, triangles, and circles. They also find the circumference of circles. Students classify solids and find the volume and surface area of rectangular prisms. find the area of a parallelogram find the area of a triangle find the circumference of a circle find the area of a circle classify solids 46

47 find the surface area of a prism find the volume of a rectangular prism [State Standard/IMAF: ; ; ; ; ; ] Chapter 11: Integers Chapter Overview: In this chapter, students compare and order integers. Next, they add, subtract, multiply, and divide integers. Finally, students use their knowledge of integers to plot points in the coordinate plane and do translations, reflections, and rotations in the plane. compare and order integers add integers subtract integers multiply integers divide integers graph points with negative coordinates learn how to recognize reflections and rotations [State Standard/IMAF: ; ; ; ; ] Chapter 12: Equations and Functions Chapter Overview: In this chapter, students first write variable expressions and equations. They then solve one-step equations by undoing operations in order to isolate the variable. Also, students are introduced to the concept of a function, and they explore that idea using input-output tables as well as ordered pairs, function rules, and graphs. write variable expressions and equations solve one-step addition equations solve one-step subtraction equations solve multiplication and division equations evaluate functions and write function rules graph linear functions in a coordinate plane [State Standard/IMAF: ; ; ; ; ; ; ; ] 47

48 Chapter 13: Probability and Statistics Chapter Overview: In this chapter, students find the probability of an event, and the complement of an event. They also use tree diagrams and tables to list outcomes. They use their knowledge of outcomes to find the probability of independent events. Students look at misleading statistics, and they learn to make stem-and-leaf plots and box-andwhisker plots. Finally, students use their knowledge of data to choose appropriate displays for data. write probabilities use diagrams, tables, and lists to find outcomes find the probability of two independent events recognize how statistics can be misleading organize data using stem-and-leaf plots represent data using box-and-whisker plots choose appropriate data displays [State Standard/IMAF: ; ; ; ] 48

49 7 th Grade Math Curriculum The following materials form the core of this math program: McDougal Littell Middle School Math Course 2 Teacher s Resource Package: Chapter Resource Books (one for each chapter, organized by lesson) Assessment Book Note Taking Guide Teacher s Edition Practice Workbook Teacher s Edition Teacher Survival Kit (includes the Professional Development Book, the Special Activities Book, and the Poster Package) Warm-Up Transparencies with Daily Homework Quiz Worked-Out Solution Key Technology: provides instruction, practice, and learning support Chapter 1: Number Sense, Patterns, and Algebraic Thinking Chapter Overview: In this chapter students describe patterns and use them to solve problems. Students also apply the order of operations to evaluate variable expressions involving powers and exponents and to solve equations. They use these skills to find the perimeter and area of rectangles and to solve real-world problems. describe patterns using whole number operations evaluate variable expressions write repeated multiplication using exponents evaluate expressions involving two or more operations use mental math to solve an equation use formulas to find perimeter and area use a 4-step plan to solve many kinds of problems [State Standard/IMAF: ; ; ; ; ; ; ] Chapter 2: Decimal Operations Chapter Overview: In this chapter students describe perform operations with decimals, including comparing and rounding decimals. Students then apply these skills to solving real-world problems involving scientific notation and metric measurements. compare, order, and rounded numbers add and subtract decimals multiply decimals divide decimals 49