Milwaukee Public Schools Curriculum Guide -Grade 5 Houghton Mifflin Math Expressions1st Quarter
Houghton Mifflin Expressions
Grade 5
2007–2008 Mathematics Curriculum Guides
Wisconsin Mathematics Standard / MPSLearning Target / Wisconsin Assessment
Descriptors for Mathematics
(For Beginning Grade 1) / 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.
Time / Curricular Connections
Units/Lessons / MPS Learning Targets / Wisconsin State Framework Assessment Descriptors / Connections
District Model CABS
September
19 teaching days
September
19 teaching days
October
20 teaching days
October
20 teaching days
October
20 teaching days
November
7 teaching days / Unit 1 Basic Multiplication and Division
1.1 Multiplication as Equal Groups (NO&R)
1.2 Arrays and Area (NO&R)
1.3 Explore the Multiplication Tables (NO&R, AR)
1.4 Make Combinations (NO&R, AR, Stats/Prob)
1.5 Understand Comparisons (NO&R, AR)
1.6 Practice with Multiplication Problems (NO&R, AR)
1.7 Discover Multiplication Patterns (NO&R)
1.8 Functions (AR)
1.9 Multiplication Strategies (NO&R)
1.10 Multiplication and Division Practice (NO&R)
1.11 Write Word Problems (NO&R)
1.12 Equations with Parentheses (NO&R, AR)
1.13 Combinations and Comparisons (NO&R, AR, Stats/Prob)
1.14 Practice with Factors (NO&R)
1.15 Multiple Step Problem (NO&R, AR)
1.16 Properties of Multiplication (NO&R, AR)
Measurement
Mini Unit APerimeter and Area
A.1 Square Units and Area (M)
Measurement
Mini Unit APerimeter and Area
A.2 Perimeter and Area of Rectangles (M)
A.3 Area of Right Triangles and Parallelograms (M,G)
A.4 The Area of Any Triangle (M,G)
A.5 Consolidate Perimeter and Area (M)
A.6 Customary Units of Length (M)
Unit 2
Addition and Subtraction with Whole Numbers and Decimals
2.1 Thousands to Thousandths (NO&R)
2.2 Equate and Compare (NO&R)
2.3 Use Decimal Numbers (NO&R)
2.4 Billions to Billionths (NO&R)
2.5 Use Place Value (NO&R)
2.6 Add Whole Numbers and Decimals (NO&R)
2.7 Addition to the Millions (NO&R)
2.8 Subtract Whole and Decimal Numbers (NO&R)
2.9 Place Value Word Problems (NO&R)
Unit 2
Addition and Subtraction with Whole Numbers and Decimals
2.10 Properties and Strategies (AR)
2.11 Pictographs With Large Numbers (NO&R, Stats/Prob)
2.12 Round Numbers on Graphs (NO&R, M)
2.13 Bar Graph and Rounding (Stats/Prob)
Unit 2
Addition and Subtraction with Whole Numbers and Decimals
Unit 2
Addition and Subtraction with Whole Numbers and Decimals
2.14 Introduce Line Graphs (Stats/Prob)
2.15 Graphs With Decimal Numbers (Stats/Prob)
2.16 Classify Word Problems (AR)
2.17 Situation and Solution Equations (AR)
2.18 Comparison Problems (AR)
2.19 Two-Step Word Problems (NO&R, Stats/Prob) / Numbers Operations and
Relationships #1
Pose real-world problems, and use strategies, including number theory concepts and place value, to compare numbers, make estimates, and solve single and multi-step word problems. (1.1, 1.2, 1.3,1.4, 1.5, 1.6, 1.7, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16)
Algebraic Relationships #8
Represent, extend, and describe patterns and functional relationships using words, symbolic rules, tables, and graphs. (1.5, 1.7, 1.8, 1.9, 1.14, 1.15)
Algebraic Relationships #9
Apply and justify use of equations, inequalities, properties (e.g., distributive, 4x27=4x25+4x2), and order of operations to represent and solve one-step and two-step problems with and without context.
(1.3, 1.4, 1.5, 1.6, 1.12, 1.13, 1.15, 1.16)
Statistics and Probability #7
Describe the difference between theoretical and experimental probabilities, determine the likelihood and fairness of events, and explain why probabilities are represented as fractions and percents from 0 to 1. (1.4, 1.13)
Measurement # 5
Compare measurement attributes and elapsed time, explain estimates, selection of unit, and conversions of measures, and determine measurements (e.g., area, size of angles, elapsed time) with tools and scales to specified degrees of accuracy(A.1)
Numbers Operations and
Relationships #1
Pose real-world problems, and use strategies, including number theory concepts and place value, to compare numbers, make estimates, and solve single and multi-step word problems. (2.1, 2.2, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9)
Numbers Operations and
Relationships #2
Generate and represent equivalent forms of commonly used fractions, decimals, and percents; estimate with benchmarks; and use strategies to compare, add, and subtract fractions and decimals with and without context.(2.1, 2.2, 2.3, 2.9)
Geometry #3
Describe, construct, and classify polygons and polyhedrons using properties (e.g., angles, lines of symmetry, parallel lines, similarity) of plane and coordinate geometry. (A.3, A.4 A.5))
Measurement # 5
Compare measurement attributes and elapsed time, explain estimates, selection of unit, and conversions of measures, and determine measurements (e.g., area, size of angles, elapsed time) with tools and scales to specified degrees of accuracy.
(A.2, A.3, A.4, A.5, A.6, 2.3, 2.12)
Statistic and Probability # 6
Conduct data investigations, interpret and summarize (e.g., mean, median, mode, range) data sets and displays (e.g., line plots, Venn diagrams), and make context-based conclusions and predictions.(2.11, 2.13)
Algebraic Relationships #9
Apply and justify use of equations, inequalities, properties (e.g., distributive, 4x27=4x25+4x2), and order of operations to represent and solve one-step and two-step problems with and without context.
(2.10)
Numbers Operations and
Relationships #1
Pose real-world problems, and use strategies, including number theory concepts and place value, to compare numbers, make estimates, and solve single and multi-step word problems(2.19)
Statistic and Probability # 6
Conduct data investigations, interpret and summarize (e.g., mean, median, mode, range) data sets and displays (e.g., line plots, Venn diagrams), and make context-based conclusions and predictions(2.14, 2.15, 2.19)
Algebraic Relationships #9
Apply and justify use of equations, inequalities, properties (e.g., distributive, 4x27=4x25+4x2), and order of operations to represent and solve one-step and two-step problems with and without context(2.16, 2.17, 2.18) / Number Operations and Relationships
B.a:4 Identify and use number theory concepts:
- Prime and composite numbers
- Divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10).
- Least common multiples
- Greatest common factor of two numbers (1.4)
B.b:13 Use all operations in everyday situations to solve single or multi-step word problems. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.12, 1.13, 1.15, 1.16)
Measurement
D.a:1 Identify appropriate units to measure length, liquid capacity, volume, time, weight/mass, temperature, including measures. Units include: inches, feet, yards, (i.e. 1 foot 3 inches) miles, centimeters, millimeters, meters, kilometers, ounces, cups, quarts, gallons, liters, hours, minutes, seconds (i.e. 1 hour 15 minutes), days, months, years, ounces, pounds, grams, kilograms, and degrees Fahrenheit/Celsius. (A.1)
D.a:2 Compare attributes of length, volume, and weight by observation or when given actual measurements (A.1)
D.a:3 Make measurement conversions within a system between units (e.g., feet and yards; inches and yards; quarts and gallons; meters and centimeters; seconds and hours(A.1)
D.c:9 Determine the area of regular shapes including right triangles. (A.1)
Statistics and Probability
E.b:10 Describe and determine the number of combinations of selecting three items from four or more items.(1.4,1.13)
Algebraic Relationships
F.a:1 Recognize, extend, describe, create and replicate a variety of patterns including attribute, numeric, and geometric patterns (1.7)
F.a:2 Represent patterns and relationships with pictures, tables, and charts (1.5)
F.a:3 Describe a rule that explains a functional relationship or pattern using addition, subtraction, or multiplication rules (1.8, 1.9, 1.14)
F.b:7 Solve one-step equations with “box” variable and whole number coefficients in problems with and without context using whole number coefficients (1.4, 1.5, 1.6)
F.b:8 Solve two-step multi-operation equations with “box” or letter variable and whole number coefficients with and without context. Ex: 3 * “box” + 1 = 7 (1.15)
F.b:9 Represent problem situations with one or two-step equations or expressions. Solve simple two-step, two-operation patterns (1.3, 1.4, 1.5, 1.6, 1.12 ,1.13, 1.15)
F.b:11 Solve equations involving any two operations. (1.12)
F.c:12 Use the commutative property of multiplication with positive single digits (1.3)
F.c:13 Use the inverse relationship of division and multiplication with single whole digits. (1.3, 1.4, 1.6, 1.16
F.c:14 Simplify (evaluate) two-step numerical expressions using correct order of operations (1.12, 1.15)
F.c:15 Demonstrate understanding of distributive property (1.16)
Numbers Operations and Relationships
B.a:1 Recognize and apply place-value concepts to whole numbers less than 10,000,000. (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.9)
B.a:2 Read, write, and represent numbers using words, numerals, pictures (base-ten blocks), number lines, arrays expanded forms (12,436=10,000+2,000+400+30+6), and symbolic reasoning e.g., 12,436=12,450-14(2.1, 2.2, 2.4, 2.5)
B.a:3 Compare and order numbers less than 100,000 represented in numbers, arrays, symbols (<, >, =) and words.
(2.2, 2.4)
B.a:12 Identify and represent equivalence between fractions, percents, and decimals.
(2.1, 2.2)
B.b:13 Use all operations in everyday situations to solve single or multi-step word problems. (2.8, 2.9)
B.b:14: Solve three and four-digit addition and subtraction with regrouping, multiplication of three-digit by two-digit numbers, division with single-digit divisors and four-digit dividends with two-step or mixed operation problems.(2.6, 2.7,2.8,2.9)
Number Operations and Relationships
B.b:15 Compute with decimals in the context of money and make change(2.1, 2.3, 2.6)
B.b 19 Estimate using basic whole number operations, benchmark fractions, and benchmark decimals. (2.9, 2.12)
Geometry
C.a:1 Recognize and name polygons with 3, 4, 5, 6 or 8 sides. (A.3, A.4, A.5)
C.a:2 Identify lines and line segments in a plane figure. (A.4)
C.a: 3 Classify plane figures by characteristics of angles (acute, obtuse, and right) and describe rays found in open-angle situations. (A.3, A.4)
C.b:5 Identify figures that are congruent and/or similar. (A.5)
Measurement
D.a:1 Identify appropriate units to measure length, liquid capacity, volume, time, weight/mass, temperature, including measures. Units include: inches, feet, yards, (i.e. 1 foot 3 inches) miles, centimeters, millimeters, meters, kilometers, ounces, cups, quarts, gallons, liters, hours, minutes, seconds (i.e. 1 hour 15 minutes), days, months, years, ounces, pounds, grams, kilograms, and degrees Fahrenheit/Celsius. (A.6)
D.a:2 Compare attributes of length, volume, and weight by observation or when given actual measurements.(A.6)
D.a:3 Make measurement conversions within a system between units (e.g., feet and yards; inches and yards; quarts and gallons; meters and centimeters; seconds and hours(A.6, 2.3)
D.b:4 Measure down to the nearest 1/8-inch, centimeter, or millimeter.
(A.5, 2.3)
D.b:7 Determine and compare elapsed time in problem-solving situations. (2.12)
D.c:9 Determine the area of regular shapes including right triangles. (A.2, A.3, A.4, A.5, A.6)
Number Operations and Relationships
B.b:13 Use all operations in everyday situations to solve single or multi-step word problems(2.19)
Statistics and Probability
E.a:2 Collect, organize, and display data in appropriate graphs or charts(2.14, 2.15)
E.a:3 Draw reasonable conclusions based on contextual data(2.14, 2.15)
E.a:5 Extract, interpret, and analyze data from single bar graphs, tables and charts, line plots, context, circle graphs, and Venn diagrams(2.14, 2.15)
E.a:6 Describe a given set of data of ten or fewer items/numbers using the terms mean, median, mode, and range to extract information from organized charts, tables, graphs, and Venn diagrams in problems with and without context(2.19)
Algebraic Relationships
F.b:7 Solve one-step equations with “box” variable and whole number coefficients in problems with and without context using whole number coefficients (2.17)
F.b:9 Represent problem situations with one or two-step equations or expressions. Solve simple two-step, two-operation patterns (2.16, 2.17, 2.18) / MPS Number Operations and Relationships CABS
# 5, # 6
MPS Algebraic Relationships CABS
# 1
MPS Statistics and ProbabilityCABS #5
MPS Algebraic Relationships CABS #2, #3, #4, #5. #6
MPS
Measurement CABS #7
MPS Geometry CABS # 4
MPS Statistics and Probability CABS #8
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Curriculum Guide Expressions Grade 5Developed by the Milwaukee Mathematics Partnership with support
1st Quarterby the National Science Foundation under Grant No. 0314898.
Version 2.0