Grade 5 Mathematics Pacing Chart, 2006–2007
Grade 5 Mathematics Pacing Chart, 2006–2007
Wisconsin Math Standard / MPSLearning Target (Grade 5) / Wisconsin Assessment Descriptors for Mathematics
(For Beginning of Grade 6) / 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.
September
/ C. Geometry / Learning Target 3 & 43. Describe, construct, and classify polygons and polyhedrons using properties (e.g., angles, lines of symmetry, parallel lines, similarity) of plane and coordinate geometry.
4. Evaluate the results of transformations from rigid motions and movement between polyhedra and nets, and describe three-dimensional figures from multiple perspectives. / Sub-skill C.a: Describing figures
1) Recognize and name polygons with 3, 4, 5, 6 or 8 sides.
2) Identify lines and line segments in a plane figure.
3) Classify plane figures by characteristics of angles (acute, obtuse, and right) and describe rays found in open-angle situations.
Sub-skill C.b: Spatial relationships and transformations
4) Use tangrams to describe, model, and construct plane figures
5) Identify figures that are congruent and/or similar.
7) Use slides, flips, and turns on figures. Identify congruent shapes using figures that have been manipulated by one or two motions (slides, flips, and turns).
8) Identify lines of symmetry and the number of lines of symmetry in figures, and design shapes that have at least one line of symmetry.
D. Measurement / Learning Target 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. / Sub-skill D.a: Measurable attributes
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).
Sub-skill D.b: Direct measurement
5) Determine angle measurement to nearest five degrees using a protractor.
Sub-skill D.c: Indirect measurement
9) Determine the area of regular shapes including right triangles.
October / B. Number Operations andRelationships
Note: Keep the focus on whole numbers. Integrate algebra descriptors into the number work. / Learning Target 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. / Sub-skill B.a: Concepts
1) Recognize and apply place-value concepts to whole numbers less than 10,000,000.
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.
3) Compare and order numbers less than 100,000 represented in numbers, arrays, symbols (<, >, =) and words.
Sub-skill B.b: Computation
13) Use all operations in everyday situations to solve single or multi-step word problems.
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.
16) Solve problems using basic multiplication and division facts.
19) Estimate using basic whole number operations, benchmark fractions, and benchmark decimals.
20) Determine reasonableness of answers.
F. Algebraic Relationships / Learning Target 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. / Sub-skill F.c: Properties
12) Use the commutative property of multiplication with positive single digits.
13) Use the inverse relationship of division and multiplication with single whole digits.
15) Demonstrate understanding of distributive property.
November / D. Measurement / Learning Target 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. / Sub-skill D.b: Direct measurement
7) Determine and compare elapsed time in problem-solving situations.
F. Algebraic Relationships / Learning Target 9
Represent, extend, and describe patterns and functional relationships using words, symbolic rules, tables, and graphs. / Sub-skill F.a: Patterns, relations and functions
1) Recognize, extend, describe, create and replicate a variety of patterns including attribute, numeric, and geometric patterns.
2) Represent patterns and relationships with pictures, tables, and charts.
3) Describe a rule that explains a functional relationship or pattern using addition, subtraction or multiplication rules.
4) Describe a rule that explains a functional relationship or pattern using addition, subtraction, or multiplication rules.
5) Determine a future event in a pattern up to the tenth item when given the first five.
December / E. Statistics and Probability / Learning Target 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. / Sub-skill E.a: Data analysis and statistics
1) Formulate questions to collect, organize, and display data.
2) Collect, organize, and display data in appropriate graphs or charts.
3) Draw reasonable conclusions based on contextual data.
4) Use data to predict outcomes or trends from graphs and tables.
5) Extract, interpret, and analyze data from single bar graphs, tables and charts, line plots, context, circle graphs, and Venn diagrams.
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.
January/February / B. Number Operations andRelationships / Learning Target 1 & 2
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. 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. / Sub-skill B.a: Concepts
4) Identify and use number theory concepts:
- Prime and composite numbers
- Divisibility potential of numbers (divisors 1–10, 25)
- Least common multiples through 24
7) Equate a monetary value with its benchmark fraction and percent. (e.g., $0.25=1/4=25%)
8) Demonstrate basic understanding of proportionality in proportional contexts.
9) Read, write, identify, order, and compare mixed fractions.
10) Represent fractions using numbers, pictures, and number lines.
11) Rename improper fractions to mixed numbers in lowest terms.
12) Identify and represent equivalence between fractions, percents, and decimals.
Sub-skill B.b: Computation
17) Rename improper fractions.
18) Add and subtract fractions with unlike denominators (halves, thirds, fourths, fifths, and tenths) with sums or differences between 0 and 1.
19) Estimate using basic whole number operations, benchmark fractions, and benchmark decimals.
20) Determine reasonableness of answers.
February / D. Measurement / Learning Target 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. / Sub-skill D.a: Measurable attributes
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.
2) Compare attributes of length, volume, and weight by observation or when given actual measurements.
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).
Sub-skill D.b: Direct measurement
4) Measure down to the nearest 1/8-inch, centimeter, or millimeter.
6) Read and interpret measuring instruments to determine the measurement of objects with standard units (U.S. customary).
Sub-skill D.c: Indirect measurement
8) Estimate measurement using U.S. customary and metric measurement.
10) Determine distance between points using a scale.
March / B. Number Operations and Relationships / Learning Targets 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. / Sub-skill B.a: Concepts
5) Read, write, and identify monetary amounts represented with visual models.
6) Compare and order monetary amounts.
Sub –skill B.b: Computation
15) Compute with decimals in the context of money and make change.
19) Estimate using basic whole number operations, benchmark fractions, and benchmark decimals.
20) Determine reasonableness of answers.
March/April / B. Number Operations and Relationships / Learning Targets 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. / Sub-skill B.b: Computation
13) Use all operations in everyday situations to solve single or multi-step word problems.
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.
F. Algebraic Relationships / Learning Target 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.
Note: This work with algebra should focus on writing and solving equations using variables to represent problem situations. / Sub-skill F.a: Patterns, relations, and functions
5) Solve simple two-step, two-operation patterns. Ex: 5, 8, 6, 9, 7, 10….. (Pattern: +3–2…..)
Sub-skill F.b: Expressions, equations, and inequalities
6) Demonstrate basic understanding of equality and inequality using symbols (<, >, =) with multi-step, mixed operations.
7) Solve one-step equations with “box” variable and whole number coefficients in problems with and without context using whole number coefficients.
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.
9) Represent problem situations with one or two-step equations or expressions. Solve simple two-step, two-operation patterns.
10) Solve two-step open sentences involving all operations.
11) Solve equations involving any two operations.
Examples: 3 * 4 – 2 = ?; 12 / 3 + 1 = “box”; 5 * 2 – 1 = a
Sub-skill F.c: Properties
14) Simplify (evaluate) two-step numerical expressions using correct order of operations.
16) Demonstrate understanding of order of operations by solving two-step open sentences involving all operations.
May / E. Statistics and Probability / Learning Target 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. / Sub-skill E.b: Probability
7) Determine the likelihood of future events, predict outcomes of future events, and test predictions using data from a variety of sources.
8) Choose or design an event that is fair or unfair.
9) Determine the probability of events in context using words, percents, or fractions.
10) Describe and determine the number of combinations of selecting three items from four or more items.
Note: Review Number Descriptors I and J related to fractions.
May/June / C. Geometry / Learning Target 3 & 4
3. Describe, construct, and classify polygons and polyhedrons using properties (e.g., angles, lines of symmetry, parallel lines, similarity) of plane and coordinate geometry.
4. Evaluate the results of transformations from rigid motions and movement between polyhedra and nets, and describe three-dimensional figures from multiple perspectives.. / Sub-skill C.b: Spatial relationships and transformations
6) Describe and compare cubes, rectangular and triangular prisms, and rectangular and triangular pyramids from nets (flat patterns).
9) Identify and describe 3-dimensional figures from multiple perspectives.
Sub-skill C.c: Coordinate systems
10) Identify and plot the coordinates of locations or objects on simple one quadrant grids using numbers only for coordinates, (e.g. (3,2)).
11) Locate the fourth coordinate pair when given three vertices of a rectangle or parallelogram on a coordinate grid.
Grade 5 Pacing Chart – 8/15/06