Download B. Number Operations and Relationships Grade 5

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B. Number Operations and Relationships
Grade 5
MPS Learning Target #1
(Grade 5)
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.
Descriptors
Concepts: 1, 2, 3, 4, 5, 6,
Computation: 13, 14, 15, 16, 19, 20
MPS Learning Target #2
(Grade 5)
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.
Descriptors
Concepts: 5, 6, 7, 8, 9, 10, 11, 12
Computation: 15, 17, 18, 19, 20
Wisconsin Sub-skill Descriptors (Beginning Grade 6)
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.
4) Identify and use number theory concepts:
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Prime and composite numbers
Divisibility potential of numbers (divisors1-10, 25)
Least common multiples through 24
Greatest common factors through 50
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5) Read, write, and identify monetary amounts represented with visual models.
6) Compare and order monetary amounts.
7) Equate a monetary value with its benchmark fraction and percent. (E.g. $.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
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.
15) Compute with decimals in the context of money and make change.
16) Solve problems using basic multiplication and division facts.
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.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
C. Geometry
Grade 5
MPS Learning Target #3
(Grade 5)
Describe, construct, and classify polygons and
polyhedrons using properties (e.g., angles, lines of
symmetry, parallel lines, similarity) of plane and
coordinate geometry.
Descriptors
Describe figures: 1, 2, 3
Spatial relationships & transformations: 4, 5, 8
Coordinate systems: 10, 11
MPS Learning Target #4
(Grade 5)
Evaluate the results of transformations from rigid motions
and movement between polyhedra and nets, and describe
three-dimensional figures from multiple perspectives.
Descriptors
Spatial relationships & transformations: 6, 7, 9
Wisconsin Sub-skill Descriptors (Beginning Grade 6)
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.
6) Describe and compare cubes, rectangular and triangular prisms, and rectangular and
triangular pyramids from nets (flat patterns).
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.
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.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
D. Measurement
Grade 5
MPS Learning Target #5
(Grade 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.
Descriptors
Measurable attributes: 1,2, 3
Direct measurement: 4, 5, 6, 7
Indirect measurement: 8, 9, 10
Wisconsin Sub-skill Descriptors (Beginning of Grade 6)
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.
5) Determine angle measurement to nearest five degrees using a protractor.
6) Read and interpret measuring instruments to determine the measurement of objects with
standard units (U.S. customary).
7) Determine and compare elapsed time in problem-solving situations.
Sub-skill D.c: Indirect measurement
8) Estimate measurement using U.S. customary and metric measurement.
9) Determine the area of regular shapes including right triangles.
10) Determine distance between points using a scale.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
E. Statistics and Probability
Grade 5
MPS Learning Target #6
(Grade 5)
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.
Descriptors
Data analysis and statistics: 1, 2, 3, 4, 5, 6
MPS Learning Target #7
(Grade 5)
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.
Descriptors
Probability: 7, 8, 9, 10
Wisconsin Sub-skill Descriptors (Beginning of Grade 6)
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 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.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
F. Algebraic Relationships
Grade 5
MPS Learning Target #8
(Grade 5)
Represent, extend, and describe patterns and
functional relationships using words, symbolic rules,
tables, and graphs.
Descriptors
Patterns, relations, & functions: 1, 2, 3, 4, 5
MPS Learning Target #9
(Grade 5)
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.
Descriptors
Expression, equations, & inequalities: 6, 7, 8, 9, 10, 11
Properties: 12, 13, 14, 15, 16
Wisconsin Sub-skill Descriptors (Beginning of Grade 6)
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) Determine a future event in a pattern up to the tenth item when given the first five.
5) Solve simple two-step, two-operation patterns. Ex: 5, 8, 6, 9, 7, 8…(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.
Ex: 3 * 4 – 2 = ?
Ex: 12 / 3 + 1 = “box”
Ex: 5 * 2 – 1 = a
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.
14) Simplify (evaluate) two-step numerical expressions using correct order of operations.
15) Demonstrate understanding of distributive property.
16) Demonstrate understanding of order of operations by solving two-step open sentences
involving all operations.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.