# A Parent Guide to Mathematics - Grade 5

■ The important math concepts in 5^{th} grade are extending
the operations of addition,

subtraction, multiplication and division of whole numbers to fractions and
decimals, and

working with angle measurement. Based on Michigan Grade Level Content
Expectations,

the following describes some of the central mathematical skills and
understandings that

students should acquire by the end of fifth grade.

■ ** Number and Operations
Multiply and Divide Whole Numbers**

1. Understand how division of whole numbers with and
without remainders is

related to multiplication and how division is related to subtraction

2. Multiply a multi- digit number by a two-digit number (e.g., 2787 × 47)

3. Divide up to a four-digit number by any two-digit number

4. Multiply one-digit and two-digit whole numbers by
powers of 10

(e.g., 26 × 10 = 260; 26 x 100 = 2600)

**Prime Factorizations
**5. Find the prime factorization of numbers from 2 through 50 and write the
results

using exponents (e.g., 24 = 2 × 2 × 2 × 3 = 2

^{3}x 3

^{1})

** Fractions and Decimals
**6. Understand fractions as division statements (e.g., 2 ÷ 3 = 2/3)

7. Express two fractions as fractions with a common
denominator (e.g., 1/2 = 3/6

and 2/3 = 4/6 )

8. Understand that decimals and percentages are forms of
fractions and be able to go

from one form to any other

9. Write fractions from applied situations in several
ways; recognize and find equivalent

ratios (e.g., 3 cups to 5 people, 3:5, an average of 3/5 cup for each person)

10. Add and subtract fractions with unlike denominators of
2 through 12 and with

denominators of 100 (e.g., 3/8 + 7/10 = 30/80 + 56/80 = 86/80)

11. Multiply one-digit and two-digit whole numbers by
decimals up to two decimal

places and by powers of 10 (e.g., 35 × 0.1 = 3.5, 8 × 0.25 = 2, 26 × 1000 =
26,000)

12. Multiply two unit fractions with small denominators (e.g., 1/3 × 1/4 = 1/12)

13. Divide a fraction by a whole number and a whole number
by a fraction, using simple

unit fractions (e.g., 1/2 ÷ 4 = 1/8 , 4 ÷ 1/2 = 8)

14. Solve applied problems involving fractions and
decimals; include rounding

answers and checking reasonableness (e.g., Gamali bought a CD for $9.99 and

the sales tax was 6%. How much did he have to pay for the CD including tax?

Answer: $10.59)

15. Solve for the unknown in equations of the form a + x = b (e.g., 1/4 + x = 7/12)

**■ Geometry and Measurement**

**Area, Volume, and Angles
**16. Use area formulas and understand and recognize the connections among the

areas of rectangles, triangles, and parallelograms

Example:

area of triangle = 1/2 (base × height)

= 1/2 (area of parallelogram)

17. Find the volume of cubes and rectangular prisms by
filling with unit cubes,

building, counting or measuring

18. Recognize the equivalence of 1 liter, 1,000 ml and
1,000 cm^{3}, make conversions

among liters, milliliters, and cubic centimeters, and know the units of measure

of volume: cubic centimeter, cubic meter, cubic inches, cubic feet, cubic yards,

and use their abbreviations (cm^{3}, m^{3}, in^{3}, ft^{3}, yd ^{3})

19. Use a protractor or angle ruler to measure angles in
degrees; classify angles

as acute (less than 90°), right (equal to 90°), obtuse (greater than 90°), or

straight (equal to 180°)

20. Find the measure of angles formed by intersecting
lines, triangles,

and quadrilaterals

**■ Data and Probability**

**Data and Graphs
**21. Construct and interpret line graphs, and

solve problems based on line graphs

(e.g., the distance-time graph shows a

3-mile trip that lasted 1 hour; the walker

traveled fast for the first 2 miles going

1 mile every 10 minutes, stopped for

20 minutes, then completed the last mile

in 20 minutes, traveling only ½ mile

for every 10 minutes)

22. Find and interpret range, mean, and mode

for a given set of data

**Glossary — Grade 5**

■ **Angle** – two rays sharing a common endpoint

■ **Exponent** – a shortcut notation to express
multiplication using the same number

several times (4 is an exponent in 3^{4} = 3 · 3 · 3 · 3 )

■** Factor** – positive whole number that divides into
a given number with zero

remainder (e.g., factors of 6 are 1, 2, 3 and 6)

■ **Line Graph** – a visual way to show how two
quantities are related to each other and

how one varies according to how the other changes

■ **Mean** – the sum of the numbers in a list divided
by the number of items in the list

(e.g., 4 is the mean of 2, 3, 4, 5, 5, 5 because 2+3+4+5+5+5=24 and 24÷6=4)

■ **Mode** – the number that occurs most often in a
list

(e.g., 5 is the mode of 2, 3, 4, 5, 5, 5)

■ **Power of Ten** – numbers whose factors can be all
tens

(e.g., 1000 = 10 x 10 x 10, so 1000 is the third power of 10)

■** Prime Number** – a whole number that has exactly
two factors; 1 and the number

itself (e.g., 2, 3, 5, 7, 11)

■ **Prime Factorization** – writing a whole number as a
product of primes

(e.g., 12 = 2 × 2 × 3)

■ **Prism** – a three-dimensional figure whose bases
(ends)

are the same size and shape and are parallel and

whose other sides are parallelograms

■ **Quadrilateral** – a polygon with four sides

Examples:

■ **Unit Fraction** – a number written in the form of
1/b, where b ≠ 0 (e.g., 1/2, 1/3, 1/4 . . .)

■ **Volume of a Rectangular Three-Dimensional Figure**
– the number of unit cubes

needed to fill up the inside of the rectangular solid

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