Milwaukee Public Schools Curriculum Guide 3 Houghton Mifflin Math Expressions Houghton Mifflin Expressions Grade 3 2008 2009 Mathematics Curriculum Guides Wisconsin Mathematics Standard MPS Learning Target Wisconsin Assessment Descriptors for Mathematics (For Beginning Grade 4) Curriculum Throughout The Year A. Mathematical Processes Note: Mathematical processes need to be embedded in all mathematical strands throughout the school year. Math processes are assessed on the WKCE-CRT and reported as a separate proficiency area. For example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. 1) Reasoning: Use reasoning and logic to: Perceive patterns Identify relationships Formulate questions Pose problems Make conjectures Justify strategies Test reasonableness of results 2) Communication: Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models). 3) Connections: Connect mathematics to the real world as well as within mathematics. 4) Representations: Create and use representations to organize, record, and communicate mathematical ideas. 5) Problem Solving: Solve and analyze routine and non-routine problems.
Unit 1 17 days Unit 1 Place Value and Multi-Digit Addition and Subtraction 1.1 Make Place Value Drawings (NO&R) 1.2 Building Numbers & Represent Money Amounts (NO&R) 1.3 Place Value & Word Problems (NO&R) 1.4 Practice with Place Value (NO&R) 1.5 Explore Multi-Digit Addition (NO&R) 1.6 Discuss Addition Methods (NO&R) 1.7 Addition with Dollars and Cents (NO&R) 1.8 The Grouping Concept in Addition (NO&R) 1.9 Practice Addition(NO&R) 1.10 Ungroup to Subtract(NO&R) 1.11 Subtract Across Zeros (NO&R) 1.12 Discuss Methods of Subtracting (NO&R) 1.13 Relate Addition and Subtraction (NO&R) 1.14 Subtraction Practice(NO&R) 1.15 Addition and Subtraction Practice (NO&R) Relationships #1 Communicate and use fluent and flexible strategies to represent and compare numbers, estimate, and solve real-world addition and subtraction problems including money. (1.1, 1.2, 1.3, 1.4 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15) Relationships B.a:1 Recognize and apply place-value concepts to whole numbers less than 10,000. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15) B.a:2 Read, write, and represent numbers using words, numerals, pictures (e.g., base ten blocks), number lines, arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6,1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13,1.14, 1.15) B.a:3 Compare and order whole numbers less than 10,000. (1.1) B.a:5 Count, compare, and make change up to $10.00 using a collection of coins and one-dollar bills. (1.2, 1.7, 1.8, 1.9, 1.11, 1.12, 1.13,1.14, 1.15) B.b:8 Use addition and subtraction in everyday situations and solve one- and two-step word problems. (1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15) B.b:9 Solve double and triple digit addition and subtraction problems with regrouping, in horizontal and vertical format in problems with and without context. (1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13,1.14, 1.15) B.b:15 Determine reasonableness of answers. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14 MPS Number Operations and Relationships CABS #5 and #7 2
Unit A Unit A Lines, Line Segments and Quadrilaterals A.1 Measure Line Segments and Perimeters of Figures (M, G) A.2 Parallel and Perpendicular Lines and Line Segments (M, G) A.3 Parallelograms, Rectangles, Squares, and Rhombuses (M, G) A.4 Draw Parallelograms and Rectangles (M, G) A.5 Classify Quadrilaterals (M, G) Geometry #4 Describe, compare, and use properties of polygons (2-D) and polyhedra (3-D) when they are combined, decomposed, and transformed (e.g., slides, flips, and turns), and identify locations of figures on a coordinate system (A.1, A.2, A.3, A.4, A.5) Measurement #5 Use appropriate standard and non-standard units to compare and estimate measurable attributes of objects, including area and perimeter, and make simple unit conversions within a measurement system. (A.1, A.2) Geometry C.a:1 Identify, describe and compare properties of 2 and 3 dimensional figures such as squares, triangles, rectangles, pentagon, hexagon, octagon, pattern block shapes, circles, cubes, pyramids, rectangular prisms, tetrahedrons, cylinders, and spheres (e.g. comparing sides, faces, corners, and edges). (A.1, A.2, A.3, A.4, A.5, ) C.b:2 Create and identify 2-dimensional geometric shapes by combining or decomposing other shapes. (A.1, A.2. A.4, A.5) Measurement D.a:1 Describe attributes of length, time, temperature, liquid capacity, weight/mass, volume and identify appropriate units to measure them. Units include: inches, feet, yards, miles, meters, centimeters, millimeters, cups, quarts, gallons, liters, seconds, minutes, hours, days, months, years, ounces, pounds, grams and degrees Fahrenheit/Celsius. (A.1, A.2) D.b:4) Read and interpret measuring instruments to determine the measurement of objects with non-standard and standard units to the nearest centimeter, 1/4-inch. (A.1, A.2) D.b: 8 Investigate measurements of area and perimeter. (A.1) MPS Measurement CABS #2 3
Unit 2 13 days Unit 2 Addition and Subtraction Word Problems 2.1 Addition and Subtractions Situations (NO&R, AR) 2.2 Word Problems with Unknown Partners (NO&R, AR) 2.3 Word Problems with Unknown Starts (NO&R, AR) 2.4 Comparison Problems(NO&R, AR) 2.5 Comparison Problems with Misleading Language (NO&R, AR) 2.6 Multi-Digit Unknown Partner and Unknown Start Problems (NO&R, AR) 2.7 Multi-Digit Comparison Problems (NO&R, AR) 2.8 Mixed Multi-Digit Word Problems (NO&R, AR) Relationships #1 Communicate and use fluent and flexible strategies to represent and compare numbers, estimate, and solve real-world addition and subtraction problems including money (2.1, 2.2, 2.3, 2.4, 2.5,.2.6, 2.7, 2.8) Algebraic Relationships #10 Explain the meaning of the equals sign, use symbols to represent problem situations, and use properties and relationships to solve open and true/false number sentences (2.1, 2.2, 2.3, 2.4, 2.5,.2.6, 2.7, 2.8) Relationships B.a:1 Recognize and apply place-value concepts to whole numbers less than 10,000. (2.7) B.a:2 Read, write, and represent numbers using words, numerals, pictures (e.g., base ten blocks), number lines, arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7. (2.7) B.a:3 Compare and order whole numbers less than 10,000. (2.4, 2.5, 2.6, 2.7, 2.8) B.b:8 Use addition and subtraction in everyday situations and solve one- and two-step word problems. (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) B.b:9 Solve double-and triple-digit addition and subtraction problems with regrouping in horizontal and vertical format in problems with and without context. (2.6, 2.7, 2.8) Algebraic Relationships F.b:3 Demonstrate an understanding that the = sign means the same as by solving open or true/false number sentences. (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) F.b:4 Use notation to represent mathematical thinking: letter or box (variable); operation symbols (+,-,=). (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) F.b:5 Demonstrate a basic understanding of equality and inequality using symbols (<.>,=) with simple addition and subtraction. (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) 4
F.c:6 Use properties and relationships of arithmetic to determine what number goes in a box to make a number sentence true. (2.1. 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) Identify property of zero. Ex: 12 + 0 = box Identify property of one. Ex: 5 x 1 = box Commutative property for addition of single-digits Associative property F.c:7 Use simple equations in a variety of ways to demonstrate the properties. (2.1, 2.2, 2.3) 5
Unit B 4 days Unit B Figures, Angles and Triangles B.1 Symmetry and Congruence (G) B.2 Label Figures and Draw Diagonals (G) B.3 Angles and Triangles (G) B.4 Angle Measures (G) Geometry #4 Describe, compare, and use properties of polygons (2-D) and polyhedra (3-D) when they are combined, decomposed, and transformed (e.g., slides, flips, and turns), and identify locations of figures on a coordinate system (B.1, B.2, B.3, B.4) Geometry C.a:1 Identify, describe and compare properties of 2 and 3 dimensional figures such as squares, triangles, rectangles, pentagon, hexagon, octagon, pattern block shapes, circles, cubes, pyramids, rectangular prisms, tetrahedrons, cylinders, and spheres (e.g. comparing sides, faces, corners, and edges). (B.1, B.2, B.3, B.4) C.b:2 Create and identify 2-dimensional geometric shapes by combining or decomposing other shapes. (B.1, B.2, B.3, B.4) C.b:4 Apply concepts of single-motion geometry (e.g., slides, flips, and turns) to match two identical shapes. (B.1, B.2) MPS Geometry CABS #4 6
Unit 3 18 days Unit 3 Use Addition and Subtraction 3.1 Round to the Nearest Hundred (NO&R) 3.2 Round to the Nearest Ten (NO&R) 3.3 Compare Whole Numbers (NO&R) 3.4 Money Values (NO&R) 3.5 Represent Money Amounts in Different Ways (NO&R) 3.6 Make Change (NO&R) 3.7 Round Money Amounts (NO&R) 3.8 Ask Addition and Subtraction Questions from Tables (NO&R, SP) 3.9 Complete Tables (NO&R, SP) 3.10 More Practice with Tables (NO&R, SP) 3.11 Word Problems with Extra or Hidden Information (NO&R) Relationships #1 Communicate and use fluent and flexible strategies to represent and compare numbers, estimate, and solve real-world addition and subtraction problems including money (3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.11, 3.12, 3.13, 3.14) Statistics and Probability #7 Formulate questions that lead to real-world data investigations, collect, organize, and display data, and draw reasonable conclusions based on the data. (3.8, 3.9, 3.10, 3.15, 3.16, 3.17) Relationships B.a:1 Recognize and apply place-value concepts to whole numbers less than 10,000. (3.1, 3.2, 3.3) B.a:5 Count, compare, and make change up to $10.00 using a collection of coins and one-dollar bills (3.4, 3.5, 3.6, 3.7) B.a:8 Use addition and subtraction in everyday situations and solve one- and two-step word problems (3.8,3.11, 3.12, 3.13, 3.14,) Statistics and Probability E.a:1 Answer and pose questions about collecting, organizing, and displaying data. Work with data in the context of realworld situations by formulating questions that lead to data collection and analysis and determining what data to collect and when and how to collect the data (3.8, 3.9, 3.10, 3.15, 3.16, 3.17) E.a:2 Collect, organize, and display data in simple bar graphs and charts including translating data from one form to the other (3.10, 3.17) E.a:4 Read, use information, and draw reasonable conclusions from data in graphs, tables, charts, and Venn diagrams (3.8, 3.9, 3.17) MPS Number Operations and Relationships CABS #5 and #7 MPS Algebra CABS #7 7
Unit 3 Use Addition and Subtraction (cont.) 3.12 Word Problems with Not Enough Information (NO&R) 3.13 Solve Two-Step Word Problems (AR) 3.14 Solve Multi-Step Word Problems (NO&R) 3.15 Read and Create Bar Graphs (SP) 3.16 Read and Create Bar Graphs with Multi-Digit Numbers (SP) 3.17 Data Day (SP) 8
Unit C 4 days Unit C Patterns C.1 Motion Geometry Patterns (G, AR) C.2 Repeating Patterns (G, AR) C.3 Growing and Shrinking Patterns (AR) Geometry #4 Describe, compare, and use properties of polygons (2-D) and polyhedra (3-D) when they are combined, decomposed, and transformed (e.g., slides, flips, and turns), and identify locations of figures on a coordinate system. (C.1, C.2) Algebraic Relationships #9 Describe, extend, and make generalizations about geometric and numeric patterns, including odd and even numbers. (C.1, C.2, C.3) Geometry C.b:4 Apply concepts of single-motion geometry (e.g., slides, flips, and turns) to match two identical shapes. (C.1, C.2) Algebraic Relationships F.a:1 Recognize, extend, describe, create, and replicate a variety of patterns including attribute, number and geometric patterns. Such as: Picture patterns Patterns in tables and charts What s-my-rule? patterns Patterns using addition and subtraction rules Focusing on relationships within patterns as well as extending patterns e.g., patterns and relationships represented with pictures, tables and charts; what s-myrule? patterns using addition and subtraction rules. (C.1, C.2, C.3) MPS Geometry CABS #4 MPS Algebra CABS #8 9
Unit 4 16 days Unit 4 Multiplication and Division with 0-5, 9 and 10 4.1 Multiply with 5 (NO & R, AR) 4.2 Multiplication as Repeated Groups (NO & R, AR) 4.3 Multiplication and Arrays (NO & R, AR) 4.4 The Meaning of Division (NO & R, AR) 4.5 Multiply and Divide with 2 (NO & R, AR) 4.6 Multiply and Divide with 10 (NO&R, AR) 4.7 Multiply and Divide with 9 (NO&R, AR) 4.8 Fluency Day for 2s, 5s, 9s, and 10s (NO&R, AR) 4.9 Multiply and Divide with 3 (NO&R, AR) 4.10 Multiplication and Area (NO&R, AR, M) 4.11 Solve and Create Word Problems (NO&R, AR) 4.12 Multiply and Divide with 4 (NO&R, AR) 4.13 Use the Strategy Cards (NO&R, AR) Relationships #2 Represent and use concepts of multiplication (e.g., grouping, arrays, skip counting, repeated addition) and division (i.e., sharing, measuring, repeated subtraction) to solve problems with and without context. (4.1,4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) Measurement #5 Use appropriate standard and non-standard units to compare and estimate measurable attributes of objects, including area and perimeter, and make simple unit conversions within a measurement system. (4.10) Algebraic Relationships #9 Describe, extend, and make generalizations about geometric and numeric patterns, including odd and even numbers. (4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.16) Relationships B.a:2 Read, write, and represent numbers using words, numerals, pictures (e.g., base ten blocks), number lines, arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7. (4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) B.a:4 Count by 2s, 3s, 5s, 10s, 25s, and 100s starting with any multiple and 100s starting with any number. Identify and name counting patterns. (4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) B.b:10 Demonstrate understanding of multiplication as grouping or repeated addition or arrays in problems with and without context (without context up to 5 x 9; in context products up to 100). (4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) B.b:11 Demonstrate understanding of the concept of division as repeated subtraction, partitioning/sharing, or measuring (dividend up to 45 and divisors up to 5). (4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) Measurement D.b:8 Investigate measurements of area and perimeter. (4.10) MPS Number Operations and Relationships CABS #1, #5, #6, #8 and #9 MPS Algebra CABS #4, #7, #8 and #12 10
Unit 4 Multiplication and Division with 0-5, 9 and 10 (cont.) 4.14 Multiply and Divide with 1 and 0 (NO&R, AR) 4.15 Play Multiplication and Division Games (NO&R) 4.16 Practice with 0s, 1s, 2s, 3s, 4s, 5s, 9s, and 10s (NO&R, AR) Algebraic Relationships #10 Explain the meaning of the equals sign, use symbols to represent problem situations, and use properties and relationships to solve open and true/false number sentences. (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.16) Algebraic Relationships F.a:1 Recognize, extend, describe, create, and replicate a variety of patterns including attribute, number and geometric patterns. Such as: Picture patterns Patterns in tables and charts What s-my-rule? patterns Patterns using addition and subtraction rules Focusing on relationships within patterns as well as extending patterns e.g., patterns and relationships represented with pictures, tables and charts; what s-my-rule? patterns using addition and subtraction rules. (4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) F.b:3 Demonstrate an understanding that the = sign means the same as by solving open or true/false number sentences. (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16) F.b:4 Use notation to represent mathematical thinking: letter or box (variable); operation symbols (+,-,=).(4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14) F.b:5 Demonstrate a basic understanding of equality and inequality using symbols (<.>,=) with simple addition and subtraction. (4.1, 4.5, 4.7, 4.9, 4.10, 4.12, 4.13, 4.14, 4.16) F.c:6 Use properties and relationships of arithmetic to determine what number goes in a box to make a number sentence true. (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14) Identify property of zero. Ex: 12 + 0 = box Identify property of one. Ex: 5 x 1 = box Commutative property for addition of single-digits Associative property F.c:7 Use simple equations in a variety of ways to demonstrate the properties. (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14) 11
Unit D 4 days Unit D Area and Perimeter D.1 Explore Perimeter and Area (NO&R,G,M,AR) D.2 Relate Area and Perimeter (NO&R,G,M,AR) D.3 Formulas for Area and Perimeter (G, M, NO&R, AR) Relationships #1 Communicate and use fluent and flexible strategies to represent and compare numbers, estimate, and solve real-world addition and subtraction problems including money. (D.1, D.2, D.3) Relationships #2 Represent and use concepts of multiplication (e.g., grouping, arrays, skip counting, repeated addition) and division (i.e., sharing, measuring, repeated subtraction) to solve problems with and without context. (D.1, D.2, D.3) Geometry #4 Describe, compare, and use properties of polygons (2-D) and polyhedra (3-D) when they are combined, decomposed, and transformed (e.g., slides, flips, and turns), and identify locations of figures on a coordinate system. (D.1, D.2, D.3) Relationships B.a:2 Read, write, and represent numbers using words, numerals, pictures (e.g., base ten blocks), number lines, arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7. (D.1, D.2, D.3) B.a:4 Count by 2s, 3s, 5s, 10s, 25s, and 100s starting with any multiple and 100s starting with any number. Identify and name counting patterns. (D.1, D.2, D.3) B.b.: 8 Use addition and subtraction in everyday situations and solve one and two-step word problems. (D.1,D.2, D.3) B.b:10 Demonstrate understanding of multiplication as grouping or repeated addition or arrays in problems with and without context (without context up to 5 x 9; in context products up to 100). (D.1, D.2, D.3) Geometry C.a:1 Identify, describe and compare properties of 2 and 3 dimensional figures such as squares, triangles, rectangles, pentagon, hexagon, octagon, pattern block shapes, circles, cubes, pyramids, rectangular prisms, tetrahedrons, cylinders, and spheres (e.g. comparing sides, faces, corners, and edges). (D.1, D.2, D.3) MPS Measurement CABS #6, #11 and #14 12
Measurement #5 Use appropriate standard and non-standard units to compare and estimate measurable attributes of objects, including area and perimeter, and make simple unit conversions within a measurement system. (D.1, D.2, D.3) Measurement D.b:8 Investigate measurements of area and perimeter. (D.1, D.2, D3) Algebraic Relationships F.b:3 Demonstrate an understanding that the = sign means the same as by solving open or true/false number sentences. (D.1, D.2, D.3) Algebraic Relationships #10 Explain the meaning of the equals sign, use symbols to represent problem situations, and use properties and relationships to solve open and true/false number sentences. (D.1, D.2, D.3) 13
Unit 5 14 days Unit 5 Multiplication and Division with 6, 7, and 8 and Problem Solving 5.1 Multiply and Divide with 6 (NO&R, AR) 5.2 Solve Area Word Problems (G, M, NO&R) 5.3 Multiply and Divide with 8 (NO&R, AR) 5.4 Write Word Problems (M, NO&R) 5.5 Multiply and Divide with 7 (NO&R, AR) 5.6 Comparison Word Problems (NO&R, AR) 5.7 More Comparison Word Problems (NO&R, AR, SP) 5.8 Square Numbers (G, M, NO&R, AR) 5.9 Practice with 6s, 7s, and 8s (G, M, NO&R,AR) 5.10 Solve Mixed Word Problems (NO&R, AR) 5.11 Solve Multi-Step Word Problems (NO&R, AR) 5.12 Solve Complex Multi-Step Word Problems (NO&R, AR) 5.13 Play Multiplication and Division Games (NO&R, AR) 5.14 Word Problem Day (NO&R,AR,SP) Relationships #1 Communicate and use fluent and flexible strategies to represent and compare numbers, estimate, and solve real-world addition and subtraction problems including money. (5.6, 5.7, 5.10, 5.11, 5.12, 5.13, 5.14 ) Relationships #2 Represent and use concepts of multiplication (e.g., grouping, arrays, skip counting, repeated addition) and division (i.e., sharing, measuring, repeated subtraction) to solve problems with and without context. (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.14) Relationships #3 Use part-whole and set models to represent, compare, and solve problems with fractions less than, equal to, and greater than one whole. (5.6, 5.7) Relationships B.a:2 Read, write, and represent numbers using words, numerals, pictures (e.g., base ten blocks), number lines, arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7. (5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.9) B.a.:3 Compare and order whole numbers less than 10,000. (5.6, 5.7) B.a:4 Count by 2s, 3s, 5s, 10s, 25s, and 100s starting with any multiple and 100s starting with any number. Identify and name counting patterns. (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9) B.b.: 8 Use addition and subtraction in everyday situations and solve one and two-step word problems. (5.6, 5.7, 5.10, 5.11, 5.12, 5.13, 5.14) B.b:10 Demonstrate understanding of multiplication as grouping or repeated addition or arrays in problems with and without context (without context up to 5 x 9; in context products up to 100). (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9) B.b:11 Demonstrate understanding of the concept of division as repeated subtraction, partitioning/sharing, or measuring (dividend up to 45 and divisors up to 5). (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9) B.a:6 Identify a fractional part of a collection/set or parts of a whole. (5.6, 5.7) MPS Number Operations and Relationships CABS #1, #2, #3, #10 and #11 MPS Statistics and Probability CABS #13 MPS Algebraic Relationships CABS #4, #8 and #9 14
Measurement #5 Use appropriate standard and non-standard units to compare and estimate measurable attributes of objects, including area and perimeter, and make simple unit conversions within a measurement system. (5.2, 5.4) Statistics and Probability #7 Formulate questions that lead to real-world data investigations, collect, organize, and display data, and draw reasonable conclusions based on the data. (5.7, 5.14) Algebraic Relationships #9 Describe, extend, and make generalizations about geometric and numeric patterns, including odd and even numbers. (5.1, 5.2, 5.3, 5.5, 5.8, 5.9) Algebraic Relationships #10 Explain the meaning of the equals sign, use symbols to represent problem situations, and use properties and relationships to solve open and true/false number sentences. (5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.14 Geometry C.a:1 Identify, describe and compare properties of 2 and 3 dimensional figures such as squares, triangles, rectangles, pentagon, hexagon, octagon, pattern block shapes, circles, cubes, pyramids, rectangular prisms, tetrahedrons, cylinders, and spheres (e.g. comparing sides, faces, corners, and edges). (5.2, 5.4, 5.8) Measurement D.b:8 Investigate measurements of area and perimeter. (5.2, 5.4, 5.8) Statistics and Probability E.a:3 Draw reasonable conclusions based on simple interpretations of data. (5.7) E.a:4 Read, use information, and draw reasonable conclusions from data in graphs, tables, charts, and Venn diagrams (5.7, 5.14) Algebraic Relationships F.a:1 Recognize, extend, describe, create, and replicate a variety of patterns including attribute, number and geometric patterns. Such as: Picture patterns Patterns in tables and charts What s-my-rule? patterns Patterns using addition and subtraction rules Focusing on relationships within patterns as well as extending patterns e.g., patterns and relationships represented with pictures, tables and charts; what s-my-rule? patterns using addition and subtraction rules. (5.1, 5.2, 5.3, 5.5, 5.8, 5.9, 5.13, 5.14) 15
F.b:3 Demonstrate an understanding that the = sign means the same as by solving open or true/false number sentences. (5.1, 5.2, 5.3, 5.5, 5.6, 5.7, 5.9) F.b:4 Use notation to represent mathematical thinking: letter or box (variable); operation symbols (+,-,=).( 5.1, 5.2, 5.3, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12) F.b:5 Demonstrate a basic understanding of equality and inequality using symbols (<.>,=) with simple addition and subtraction. (5.3, 5.5, 5.6, 5.7, 5.9, 5.10, 5.11, 5.12) F.c:6 Use properties and relationships of arithmetic to determine what number goes in a box to make a number sentence true. (5.1, 5.2, 5.3, 5.5, 5.6, 5.7, 5.8, 5.9) Identify property of zero. Ex: 12 + 0 = box Identify property of one. Ex: 5 x 1 = box Commutative property for addition of single-digits Associative property F.c:7 Use simple equations in a variety of ways to demonstrate the properties. (5.1, 5.2, 5.3, 5.5, 5.6, 5.7, 5.8, 5.9) 16
Unit E 3 days Unit E E.1 Tell (M) E.2 Elapsed (M) E.3 Clock Angles (M) Measurement #6 Read and interpret customary and metric measuring instruments and determine time to the nearest minute and elapsed time in real-world situations. (E.1, E.2, E.3) Measurement D.b:6 Tell time to the nearest minute and translate time from analog to digital clocks and vice versa. (E.1, E.2, E.3) D.b:7 Determine and compare elapsed time in multiples of 15 minutes in problem-solving situations. (E.1, E.2, E.3) MPS Measurement CABS #9 17
Unit 6 21 days Unit 6 Exploring Fractions, Probability, and Division with Remainders 6.1 Fractions as Parts of a Whole (NO&R) 6.2 Fractions as Parts of a Set (NO&R) 6.3 Unit Fractions of Sets and Numbers (NO&R) 6.4 Compare with Fractions (NO&R, Stats/Prob) 6.5 Practice Fractional Comparisons (NO&R, Stats/Prob) 6.6 Find a Fraction of a Set or Number (NO&R) 6.7 Fractions on Circle Graphs (NO&R, AR, SP) 6.8 Probability Day (S&P) 6.9 Introduce Equivalence (NO&R) 6.10 Explore Equivalence(NO&R) 6.11 Equivalence Patterns(NO&R) 6.12 Find Equivalent Fractions by Multiplying(NO&R) 6.13 Find Equivalent Fractions by Dividing(NO&R) Relationships #2 Represent and use concepts of multiplication (e.g., grouping, arrays, skip counting, repeated addition) and division (i.e. sharing, measuring, repeated subtraction) to solve problems with and without context (6.18, 6.19, 6.20) Relationships #3 Use part-whole and set models to represent, compare, and solve problems with fractions less than, equal to, and greater than one whole. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.9, 6.10,) Statistics and Probability #7 Formulate questions that lead to real-world data investigations, collect, organize, and display data, and draw reasonable conclusions based on the data. (6.4, 6.5, 6.7) Algebraic Relationships #10 Explain the meaning of the equals sign, use symbols to represent problem situations, and use properties and Number Operations & Relationships B.a:6 Identify a fractional part of a collection/set or parts of a whole. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.9, 6.10,6.11, 6.12, 6.13, 6.14,6.15, 6.16, 6.17) B.a:7 Read, write, order, and represent unit fractions (e.g., 1/2, 1/3, 1/4) and part(s) of a set. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7,6.9, 6.10, 6.11, 6.12, 6.13, 6.14, 6.15, 6,16, 6.17) B.b:12 Use fractions to represent quantities when solving problems involving equal sharing or partitioning including fractions less than one as well as mixed numbers. (6.3, 6.4, 6.5, 6.6, 6.7, 6.9, 6.10,6.11,6.12, 6.13, 6.14, 6.15, 6.16, 6.17 ) B.b:11 Demonstrate understanding of the concept of division as repeated subtraction, partitioning/sharing, or measuring (dividend up to 45 and divisors up to 5). (6.18, 6.19, 6.20) B.b:13 Represent fractions with shaded circles, rods, squares or pictorial representations of objects (for a set). (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.9,6.10, 6.11, 6.12,6.13,6.14, 6.15, 6.17) Statistics and Probability E.a:1Answer and pose questions about collecting, organizing, and displaying data. Work with data in the context of realworld situations by formulating questions that lead to data collection and analysis and determining what data to collect and when and how to collect the data. (6.8) E.a:2 Collect, organize, and display data in simple bar graphs and charts including translating data from one form to the other. (6.8) E.a:3 Draw reasonable conclusions based on simple interpretations of data. (6.4, 6.5, 6.6, 6.8) MPS Statistics and Probability CABS #10, #11, #14, #15 18
Unit 6 Exploring Fractions, Probability, and Division with Remainders (cont.) 6.14 Add Any Fractions(NO&R) 6.15 Compare and Subtract Fractions(NO&R) 6.16 Fractions on a Number Line(NO&R) 6.17 Improper Fractions and Mixed Numbers(NO&R) 6.18 Introduce Division with Remainders(NO&R) 6.19 Understand Remainders(NO&R) 6.20 Practice Division with Remainders(NO&R) relationships to solve open and true/false number sentences. (6.7) Statistics and Probability #7 Formulate questions that lead to real-world data investigations, collect, organize, and display data, and draw reasonable conclusions based on the data. (6.8) Statistics and Probability #8 Determine the likelihood (e.g., more, less, or equally likely) and fairness of events, and describe and predict outcomes and combinations of simple events. (6.8) E.a:4 Read, use information, and draw reasonable conclusions from data in graphs, tables, charts, and Venn diagrams (6.4, 6.5, 6.6, 6.8) E.b:5 Determine if the occurrence of future events are more, less, or equally likely to occur. (6.8) E.b:6 Design a fair and an unfair spinner. (6.8) E.b:7 Predict the outcomes of a simple event using words to describe probability. Ex: Flipping a coin has a 1 out of 2 chance of getting a head. (6.8) E.b:8 Describe and determine the number of combinations for choosing 2 out of 3 items. Ex: Red hat, blue jacket and green jacket. What are the combinations of wearing a hat and a jacket? (6.8) Algebraic Relationships F.b:3 Demonstrate an understanding that the = sign means the same as by solving open or true/false number sentences. (6.7) F.b:4 Use notation to represent mathematical thinking: letter or box (variable); operation symbols (+,-,=).(6.7) 19
Unit F 5 days Unit F Three Dimensional Figures F.1 Explore Cubes (G) F.2 Two Dimensional Pictures of Three Dimensional Buildings (G) F.3 Explore Prisms, Cylinders and Pyramids (G) F.4 Explore Cones (G) F.5 Explore Circles and Spheres (G) Geometry #4 Describe, compare, and use properties of polygons (2-D) and polyhedra (3-D) when they are combined, decomposed, and transformed (e.g., slides, flips, and turns), and identify locations of figures on a coordinate system.(f.1, F.2, F.3, F.4, F.5) Geometry C.a:1 Identify, describe and compare properties of 2 and 3 dimensional figures such as squares, triangles, rectangles, pentagon, hexagon, octagon, pattern block shapes, circles, cubes, pyramids, rectangular prisms, tetrahedrons, cylinders, and spheres (e.g. comparing sides, faces, corners, and edges). (F.1, F.3, F.4, F.5) C.b:3 Identify cubes and square pyramids from their nets (flat patterns). (F.1, F.2, F.3) MPS Geometry CABS #1, #4, #5, and #6 20
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Unit 7 13 days Unit 7 Measurement 7.1 Customary Units of Length (M) 7.2 Inches, Feet and Yards (M) 7.3 Centimeters, Decimeters and Meters (M) 7.4 Add Lengths (M) 7.5 Customary Units of Capacity (M) 7.6 Metric Units of Capacity (M) 7.7 Improper Fractions and Mixed Numbers in Measurement (M, NO&R) 7.8 Measurement Equivalencies and Fractions (M) 7.9 Customary Units of Weight and Metric Units of Mass (M) 7.10 Temperature (M) 7.11 Estimation Day (M) Relationships #3 Use part-whole and set models to represent, compare, and solve problems with fractions less than, equal to, and greater than one whole. (7.7) Measurement #5 Use appropriate standard and non-standard units to compare and estimate measurable attributes of objects, including area and perimeter, and make simple unit conversions within a measurement system. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 7.10, 7.11) Relationships B.b: 12 Use fractions to represent quantities when solving problems involving equal sharing or portioning including fractions less than one as well as mixed numbers. (7.7) Measurement D.a:1 Describe attributes of length, time, temperature, liquid capacity, weight/mass, volume and identify appropriate units to measure them. Units include: inches, feet, yards, miles, meters, centimeters, millimeters, cups, quarts, gallons, liters, seconds, minutes, hours, days, months, years, ounces, pounds, grams and degrees Fahrenheit/Celsius. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 7.10, 7.11 ) D.a:2 Compare attributes of length, volume and weight by observation or when given actual measurements. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 7.11) D.a:3 Make measurement conversions within a system (e.g., yards to feet; feet to inches; hours to minutes; days to hours; years to months; gallons to quarts). (7.2, 7.3, 7.5, 7.6, 7.8, 7.9, 7.11 ) D.b:4 Read and interpret measuring instruments to determine the measurement of objects with non-standard and standard units to the nearest centimeter, 1/4-inch. (7.1, 7.3, 7.4, 7.7, 7.11) D.b:5 Read thermometers to the nearest 5 degrees F/C. (7.10) D.b:8 Investigate measurements of area and perimeter.(7.4, 7.10) D.c:9 Apply estimation techniques using non-standard units. (7.2, 7.3, 7.5,7.6, 7.10, 7.11) MPS Measurement CABS #1, #3, #7, #11, #13 22
Unit G 4 days Unit G Directions and Locations G.1 Directions and Maps (G) G.2 Locate Points on a Coordinate Grid (G) G.3 Explore Line Segments and Figures on a Coordinate Grid (G) Geometry #4 Describe, compare, and use properties of polygons (2-D) and polyhedra (3-D) when they are combined, decomposed, and transformed (e.g., slides, flips, and turns), and identify locations of figures on a coordinate system. (G.1, G.2, G.3) Geometry C.c:5 Use simple 2-dimensional coordinate systems to find locations on maps and to represent points and simple figures with coordinates using letters and numbers, (e.g., (E, 3)). (G.2, G.3) C.c:6 Identify and use relationships among figures (e.g., location, position, and intersection). (G.1, G.2, G.3) MPS Geometry CABS #3 23