# NORTH MAC MIDDLE SCHOOL CURRICULUM GUIDE

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1 Teacher : Kelsie Fairfull Grade Level: 4 th Course: Math Course Description The fourth grade math curriculum will focus on multiplication and division of whole numbers (with focus on multiplication and division facts while working on multidigit multiplication and division), addition and subtraction of fractions and decimals, and identifying and describing representations of points, lines, line segments, rays, and angles, including endpoints and vertices. Concrete materials and two-dimensional representations will be used to solve problems involving perimeter, patterns, probability, and equivalence of fractions and decimals. Textbook: Title: Progress in Mathematics ISBN: Authors: Publisher: Sadlier Oxford Publication Date: 2013 Assessment There will be various points assigned each quarter. These points will be obtained from assignments, quizzes, chapter tests, and projects.

2 1-1 Thousands 1-2 Milliion 1-3 Millions 1-4 Place Value Check Your Progress Chapter Check Your Progress Chapter Check Your Progress Chapter Check Your Progress Chapter UNIT 1 Multiplication & Division Concepts Content Assessment Common Core Essential Questions 4.OA.1 Check Your Progress Use the four How and when can 4-1 A Number Patterns Chapt operations with numbers be manipulated whole numbers to for 4-1B Use Multiplication to compare Check Your Progress solve problems. application purposes? Chapt Interpret a What are ways numbers multiplication Check Your Progress are represented in Chapt 1-13 equation as a everyday life? comparison, e.g., Check Your Progress interpret 35 = 5 x 7 as How can estimation and Chapter 4 1-6A a statement that 35 is mental math aid in the 5 times as many as 7 development of number Check Your Progress and 7 times as many sense? Chapter as 5. Represent verbal statements of How can you build Check Your Progress multiplicative numbers through Chapter comparisons as hundred millions? multiplication equations. 4.NBT.1 Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten How can you use models and related facts to find missing factors?

3 1-5 Estimation 1-1 Thousands 1-3 Millions 1-4 Place Value 1-6 Compare/Order Whole Numbers 1-7 Number Sense: Number Line 1-13 Problem Solving - Mixed Check Your Progress Chapter Check Your Progress Chapter times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) 4.NBT.2 Generalize place value understanding for multi-digit whole numbers. Read and write multi-digit whole numbers using baseten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and <

4 symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) 8-6 Factors (GCF) 9-6 Multiples 9-6A Factor Pairs 9-6B Prime and Composite Numbers 4.OA.4 Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite.

5 5-15 Factor Trees (Ladders) 4-1 Multiplication Properties 4-2 Multiplication Models 4-3 Special Factors 4-4 Multiply by One-Digit Numbers 4-5 A Multiply with Models 4-6 Multiply with Regrouping 4-6A Use Mental Math to Multiply 4-7 Multiply Three-Digit Numbers 4.NBT.5 Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate

6 4-9 Multiplying Four-Digit Numbers 4-10 Patterns in Multiplication 4-11A Multiplying with Area Models 4-12 Multiply by Two-Digit Numbers 4-13 More Multiplication with Two- Digit Numbers and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) 5-13 Multi-step Problems 5-1 Division Rules 5-2 Relate Multiplication and Division 5-3 Missing Numbers 5-4 Number Patterns 5-5 Estimate in Division/ One-Digit Division 5-6 One-Digit Quotients 5-7 Divisibility Rules 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using

7 5-8/5-9 Two-Digit Quotients 5-10 Three-Digit Quotients equations, rectangular arrays, and/or area models Zeros In Quotients 5-13 Large Number Division 5-13A Multistep Problems and Bar Graphs 5-14 Division in Money 4.OA.2 5-4A Use Bar Diagrams 5-15 Order of Operations 5-16 Mean (Average) 5-17 Problem Solving-Interpret Remainders 5-18 Problem Solving - Review Problem Solving: More than one Step Problem Solving: Review Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem,

8 14-1 Equations 4-5 Products: Front End Estimation 4-7 Multiply Three-Digit Numbers 4-11 Products: Rounding and Estimation 4-16 Problem Solving Mixed Review 5-6 One-Digit Quotients 5-7 Divisibility Rules 5-8/5-9 Two-Digit Quotients 5-10 Three-Digit Quotients 5-11 More Quotients 5-12 Zeros In Quotients 5-13 Large Number Division distinguishing multiplicative comparison from additive comparison. 4.0A.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

9 5-13A Multistep Problems and Bar Graphs 6-13 Problem Solving: Use more than One Step 12-2 Divisors: Multiples of Ten 12-3 Estimate Quotients 12-4 Two-Digit Dividend 12-5 Three Digit Dividends 12-6 Trial Quotients 12-7 Greater Quotients 12-8 Four Digit Dividends 12-9 Zero in the Quotient Greater Dividends Problem Solving: More than one Step Problem Solving: Review

10 UNIT 2:Fractions: Equivalence and Operations Content Assessment Standards Common Core Essential Questions 8-3 Esitmate Fractions 8-4 Understand Equivalent Fractions 8-5 Write Equivalent Fractions 8-7 Factors: Lowest Terms 8-12 Problem Solving Applications: Review Chapter Chapter 8 6-8A Chapter Chapter Chapter 9 6-8A Chapter NF.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this How can strategies be used to compute fractions and decimals? How can fractions and decimals be modeled and compared? How are four math operations compared? Why is it important to hve quick recall of multiplication and division facts?

11 8-1 Write fractions 8-2 Fractions and number line 8-3 Estimate fractions 8-4 Understand equivalent fractions 8-8 Mixed Numbers 8-8A Compare fractions using benchmarks 8-9 Compare fractions 8-10 Order fractiosn 8-12 Problem Solving applications: Review principle to recognize and generate equivalent fractions. 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. How can you find the perimeter/area of a shape? What geometric features are present in our surroundings? 9-1A Models to Add fractions 4.NF.3a

12 9-1C Use models to subtract fractions 9-3 Improper fractions Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 9-1B Decompose fractions 9-1 Add fractions: like denominators 9-2A Word Problems with fractions 4.NF. 3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = /8 = 8/8 + 8/8 + 1/8. 4.NF.3c Add and subtract mixed numbers with like

13 9-2 Subtract fractions: like denominators 9-12 Problem solving: mixed review denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 9-8A Multiply with fractions 4.NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4). 9-8A Multiply with fractions 4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction

14 by a whole number. 9-8A Multiply with fractions 9-9 Compute probablility 9-10 Find pare of a number 9-12 Problem Solving: mixed review 4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. 6-1 Measure with Inches 6-2 Rename Units of Length 6-3 Compute customary units 6-4 Customary Units of capacity 6-5 Customary Units of weight 6-6 Measure with metric units 6-7 Work with metric units 6-8 Metric units of capacity 6-9 Metric units of mass 6-10 Temperature 6-11 A renamed measure 6-11 Time 6-12 Elapsed time 4.MD.1 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

15 2-8 Add and subtract money 4-8 Multiplying money 4-12 Multiply by two-digit numbers 5-14 Divide money 6-1 Measure with Inches 6-2 Rename Units of Length 6-3 Compute customary units 6-4 Customary Units of capacity 6-5 Customary Units of weight 6-6 Measure with metric units 6-7 Work with metric units 6-8 Metric units of capacity 6-9 Metric units of mass 6-10 Temperature 6-11 A renamed measure 6-11 Time 6-12 Elapsed time 6-13 Problem solving: more than one step 6-14 Problem solving application Divide with money 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.3 Solve problems involving measurement

16 11-1 Using Perimeter Formulas 11-2 Using Area Formulas 11-3 Perimeter and Area 11-3A Perimeter and Area Formulas 11-9 Problem Solving Application Mixed Review 7-4 Surveys and Line Plots 9-5A Organize Measurement Data and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

17 Unit 3 Unit: Decimals Content Assessment Standards Common Core Essential Questions 4.NF.5 Express a fraction What are ways numbers with denominator 10 are represented in as an equivalent everyday life? fraction with denominator 100, and How are use this technique to fractions/decimals add two fractions with related. respective denominators 10 and For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/ C Add fractions with denominators of 10 and 100 When and where do I use fractions and decimals in my daily life? 13-1 Tenths/Hundredths 13-2 Decimals Greater than One 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For How do I use customary and metric measurement in my daily life to measure length? How can measurements be used to solve problems?

18 13-3 Decimal Place Value example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 13-3A Comparing Decimals with models and symbols 13-4 Comparing decimals 13-5 Ordering decimals 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

19 Unit 4 Computation Applications 4-5 Products: Front End Estimation 4-7 Multiply Three-Digit Numbers 4-11 Products: Rounding and Estimation 4-16 Problem Solving Mixed Review 5-6 One-Digit Quotients 5-7 Divisibility Rules 5-8/5-9 Two-Digit Quotients 5-10 Three-Digit Quotients 5-11 More Quotients Content Assessment Standards Common Core Essential Questions 4.OA.3 Represent and solve Chapter 11 3A problems involving Chapter multiplication and Chapter division. Use Chapter multiplication and Chapter division within Chapter to solve word Chapter problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 4.OA.5

20 5-12 Zeros In Quotients 5-13 Large Number Division 5-13A Multistep Problems and Bar Graphs 6-13 Problem Solving: Use more than One Step 12-2 Divisors: Multiples of Ten 12-3 Estimate Quotients 12-4 Two-Digit Dividend 12-5 Three Digit Dividends 12-6 Trial Quotients 12-7 Greater Quotients 12-8 Four Digit Dividends 12-9 Zero in the Quotient Greater Dividends Problem Solving: More than one Step Problem Solving: Review Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) can be found by 3 5 = 15 then 15 2 = 30, or by 5 2 = 10 then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = 56. (Distributive property.) (Students need not use formal terms for these properties.) 4.NBT.3 Generalize place value understanding for

21 multi-digit whole numbers. Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) 4-1 Multiplication Properties 4-1A Number Patterns Problem Solving Find Pattern 4.NBT.4 Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) 4.MD.1

22 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),. 4.MD.2

23 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale

24 UNIT 5 Dimensional Geometry 10-1 Points, Lines and Line Segments 10-2 Rays and Angles 10-3 Parallel and Perpendicular Lines 10-4 Circles Content Assessment Standards Common Core Essential Questions 4.G.1 Draw points, lines, line segments, rays, angles What are ways numbers Chapter (right, acute, obtuse), are represented in and perpendicular and everyday life? Chapter parallel lines. Identify these in twodimensional Chapter figures. How do coordinate grids help you organize information? Coordinate Geometry Problem Solving Application: Mixed Review What geometric features are present in our surroundings?

25 10-1 Points, Lines, and Line Segments 10-2 Rays and Angels 10=3 Parallel and perpendicular lines 10-5 Polygons 10-6 Quadrilaterals 4.G.2 Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles 10-7 Triangles 10-7A Symmetry Problem Solving Find Pattern 4.G.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.

26 10-1A Angle Measure 10-2 Rays and Angles 4.MD.5a Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles 4.MD.5b Recognize angles as geometric shapes that

27 10-1A Angle Measure are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through n one-degree angles is said to have an angle measure of n degrees Rays and Angles 10-2A Measure Angles 10-2B Unknown Angle Measures 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum

28 of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. QUARTER: COURSE: Content Assessment Standards Common Core Essential Questions

29 QUARTER: COURSE: Content Assessment Standards Common Core Essential Questions

30 QUARTER: COURSE: Content Assessment Standards Common Core Essential Questions

31

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