Michigan State Standards for Mathematics: Grade 5

MI.N. Number and Operations

N.1. Understand division of whole numbers

N.MR.05.01. Understand the meaning of division of whole numbers with and without remainders; relate division to fractions and to repeated subtraction.

N.MR.05.02. Relate division of whole numbers with remainders to the form a = bq + r, e.g., 34 / 5 = 6 r 4, so 5 x 6 + 4 = 34; note remainder (4) is less than divisor (5).

N.MR.05.03. Write mathematical statements involving division for given situations.

N.2. Multiply and divide whole numbers

N.FL.05.04. Multiply a multi-digit number by a two-digit number; recognize and be able to explain common computational errors such as not accounting for place value.

N.FL.05.05. Solve applied problems involving multiplication and division of whole numbers.

N.FL.05.06. Divide fluently up to a four-digit number by a two-digit number.

N.3. Find prime factorizations of whole numbers

N.MR.05.07. Find the prime factorization of numbers from 2 through 50, express in exponential notation, e.g., 24 = 2 cubed x 3 to the first, and understand that every whole number greater than 1 is either prime or can be expressed as a product of primes.

N.4. Understand meaning of decimal fractions and percentages

N.ME.05.08. Understand the relative magnitude of ones, tenths, and hundredths and the relationship of each place value to the place to its right, e.g., one is 10 tenths, one tenth is 10 hundredths.

N.ME.05.09. Understand percentages as parts out of 100, use % notation, and express a part of a whole as a percentage.

N.5. Understand fractions as division statements; find equivalent fractions

N.ME.05.10. Understand a fraction as a statement of division, e.g., 2 / 3 = 2/3, using simple fractions and pictures to represent.

N.ME.05.11. Given two fractions, e.g., 1/2 and 1/4, express them as fractions with a common denominator, but not necessarily a least common denominator, e.g., 1/2 = 4/8 and 3/4 = 6/8 ; use denominators less than 12 or factors of 100.

N.6. Multiply and divide fractions

N.ME.05.12. Find the product of two unit fractions with small denominators using an area model.

N.MR.05.13. Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions.

N.7. Add and subtract fractions using common denominators

N.FL.05.14. Add and subtract fractions with unlike denominators through 12 and/or 100, using the common denominator that is the product of the denominators of the 2 fractions, e.g., 3/8 + 7/10 : use 80 as the common denominator.

N.8. Multiply and divide by powers of ten

N.MR.05.15. Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, 1,000; and identify patterns.

N.FL.05.16. Divide numbers by 10's, 100's, 1,000's using mental strategies.

N.MR.05.17. Multiply one-digit and two-digit whole numbers by decimals up to two decimal places.

N.9. Solve applied problems with fractions

N.FL.05.18. Use mathematical statements to represent an applied situation involving addition and subtraction of fractions.

N.MR.05.19. Solve contextual problems that involve finding sums and differences of fractions with unlike denominators using knowledge of equivalent fractions.

N.FL.05.20. Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness.

N.MR.05.21. Solve for the unknown in equations such as 1/4 + x = 7/12.

N.10. Express, interpret, and use ratios; find equivalences

N.MR.05.22. Express fractions and decimals as percentages and vice versa.

N.ME.05.23. Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3 : 5, 3/5; recognize and find equivalent ratios.

MI.M. Measurement

M.1. Know, and convert among, measurement units within a given system

M.UN.05.01. Recognize the equivalence of 1 liter, 1,000 ml and 1,000 cubic cm and include conversions among liters, milliliters, and cubic centimeters.

M.UN.05.02. Know the units of measure of volume: cubic centimeter, cubic meter, cubic inches, cubic feet, cubic yards, and use their abbreviations (cm3, m3, in3, ft3, yd3).

M.UN.05.03. Compare the relative sizes of one cubic inch to one cubic foot, and one cubic centimeter to one cubic meter.

M.UN.05.04. Convert measurements of length, weight, area, volume, and time within a given system using easily manipulated numbers.

M.2. Find areas of geometric shapes using formulas

M.PS.05.05. Represent relationships between areas of rectangles, triangles, and parallelograms using models.

M.TE.05.06. Understand and know how to use the area formula of a triangle: A = 1/2 bh (where b is length of the base and h is the height), and represent using models and manipulatives.

M.TE.05.07. Understand and know how to use the area formula for a parallelogram: A = bh, and represent using models and manipulatives.

M.3. Understand the concept of volume

M.TE.05.08. Build solids with unit cubes and state their volumes.

M.TE.05.09. Use filling (unit cubes or liquid), and counting or measuring to find the volume of a cube and rectangular prism.

M.PS.05.10. Solve applied problems about the volumes of rectangular prisms using multiplication and division and using the appropriate units.

MI.G. Geometry

G.1. Know the meaning of angles, and solve problems

G.TR.05.01. Associate an angle with a certain amount of turning; know that angles are measured in degrees; understand that 90 degrees, 180 degrees, 270 degrees, and 360 degrees are associated respectively, with 1/4, 1/2, and 3/4, and full turns.

G.GS.05.02. Measure angles with a protractor and classify them as acute, right, obtuse, or straight.

G.GS.05.03. Identify and name angles on a straight line and vertical angles.

G.GS.05.04. Find unknown angles in problems involving angles on a straight line, angles surrounding a point, and vertical angles.

G.GS.05.05. Know that angles on a straight line add up to 180 degrees and angles surrounding a point add up to 360 degrees; justify informally by 'surrounding' a point with angles.

G.GS.05.06. Understand why the sum of the interior angles of a triangle is 180 degrees and the sum of the interior angles of a quadrilateral is 360 degrees, and use these properties to solve problems.

G.2. Solve problems about geometric shapes

G.GS.05.07. Find unknown angles and sides using the properties of: triangles, including right, isosceles, and equilateral triangles; parallelograms, including rectangles and rhombuses; and trapezoids.

MI.D. Data and Probability

D.1. Construct and interpret line graphs

D.RE.05.01. Read and interpret line graphs, and solve problems based on line graphs, e.g., distance-time graphs, and problems with two or three line graphs on same axes, comparing different data.

D.RE.05.02. Construct line graphs from tables of data; include axis labels and scale.

D.2. Find and interpret mean and mode for a given set of data

D.AN.05.03. Given a set of data, find and interpret the mean (using the concept of fair share) and mode.

D.AN.05.04. Solve multi-step problems involving means.