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Throughout the Year
Grade 5 Mathematics Pacing Chart, 2006–2007
Wisconsin Math
Standard
MPS
Learning Target (Grade 5)
Wisconsin Assessment Descriptors for Mathematics
(For Beginning of Grade 6)
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.
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.
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.
Learning Target 1
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.
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.
September
C. Geometry
October
D.
Measurement
B. Number
Operations
and
Relationships
Pose real-world problems,
and use strategies, including
number theory concepts and
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.
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.
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.
Curriculum
Grade 5 Mathematics Pacing Chart, 2006–2007
place value, to compare
numbers, make estimates,
and solve single and multistep word problems.
3) Compare and order numbers less than 100,000 represented in numbers, arrays, symbols (<,
>, =) and words.
F. Algebraic
Relationships
Learning Target 9
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.
D.
Measurement
Learning Target 5
F. Algebraic
Relationships
Learning Target 9
November
Note: Keep the
focus on whole
numbers.
Integrate
algebra
descriptors into
the number
work.
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 twostep problems with and
without context.
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.
Represent, extend, and
describe patterns and
functional relationships
using words, symbolic rules,
tables, and graphs.
Grade 5 Pacing Chart – 8/15/06
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.
Sub-skill D.b: Direct measurement
7) Determine and compare elapsed time in problem-solving situations.
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.
Grade 5 Mathematics Pacing Chart, 2006–2007
Learning Target 6
B. Number
Operations
and
Relationships
Learning Target 1 & 2
January/February
December
E. Statistics
and
Probability
February
D.
Measurement
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.
1. Pose real-world problems,
and use strategies, including
number theory concepts and
place value, to compare
numbers, make estimates,
and solve single and multistep 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.
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.
Grade 5 Pacing Chart – 8/15/06
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.
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
Greatest common factors through 50
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.
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.
Grade 5 Mathematics Pacing Chart, 2006–2007
March/April
March
6) Read and interpret measuring instruments to determine the measurement of objects with
standard units (U.S. customary).
B. Number
Operations
and
Relationships
Learning Targets 2
B. Number
Operations
and
Relationships
Learning Targets 1
F. Algebraic
Relationships
Learning Target 9
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.
Pose real-world problems,
and use strategies, including
number theory concepts and
place value, to compare
numbers, make estimates,
and solve single and multistep word problems.
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 twostep problems with and
without context.
Note: This work with algebra
should focus on writing and
solving equations using
variables to represent problem
situations.
Grade 5 Pacing Chart – 8/15/06
Sub-skill D.c: Indirect measurement
8) Estimate measurement using U.S. customary and metric measurement.
10) Determine distance between points using a scale.
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.
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.
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
Grade 5 Mathematics Pacing Chart, 2006–2007
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.
Learning Target 7
C. Geometry
Learning Target 3 & 4
May/June
May
E. Statistics
and
Probability
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.
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 threedimensional figures from
multiple perspectives..
Grade 5 Pacing Chart – 8/15/06
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.
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.