Virginia Mathematics

2009 Grade 5 Standards of Learning

Virginia Department of EducationK-12 Mathematics Standards of Learning Institutes October 2009

Major SOL Changes

Number and Number Sense Identify and describe the

characteristics of prime and composite numbers; and

Identify and describe the characteristics of even and odd numbers.

Major SOL Changes

Computation and Estimation Find the sum, difference, product, and

quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and

Evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition, subtraction, multiplication, and division.

Major SOL Changes

Measurement Find perimeter, area, and volume in

standard units of measure; Identify equivalent measurements within

the metric system; and Estimate and then measure to solve

problems, using U.S. Customary and metric units.

Major SOL Changes

Geometry Classify triangles as right, acute, obtuse,

equilateral, scalene, or isosceles.

Major SOL Changes

Probability and Statistics Describe mean, median, and mode as

measures of center; Describe mean as fair share; and Describe the range of a set of data as a

measure of variation.

Major SOL Changes

Patterns, Functions, and Algebra Model one-step linear equations in one

variable, using addition and subtraction; and

Investigate and recognize the distributive property of multiplication over addition.

Major Changes

Related SOL have been combined to create one SOL with bulletsEX:(2001) 5.22 The student will create a problem situation based on a given open sentence

using a single variable. [Moved to new SOL 5.18 d]

(2009)5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical relationship, using

a variable; c) model one-step linear equations in one variable using addition and subtraction; and d) create a problem situation based on a given open sentence using a single variable.

Major ChangesDetails on instructional strategies have been removed for potential placement in the Curriculum FrameworkEX:(2001) 5.7 The student will add and subtract with fractions and mixed numbers, with and without regrouping, and express answers in simplest form. Problems will include like and unlike denominators limited to 12 or less [Move to Curriculum Framework].

(2009) 5.6 The student will solve single and multistep practical problems involving addition and subtraction with fractions and mixed numbers, with and without regrouping, and express answers in simplest form.

Number and Number Sense:

Sample Problem: 3/5 + 1/2

Van De Walle, (1994)

Sample Problem: 3/5 + 1/2

3/5

+

1/2

6/10

5/10

+

=

=Van De Walle, (1994)

Sample Problem: 3/5 + 1/2

3/5

1/2

+

6/10

5/10

+

=

=

Rewrite

6/10 + 5/10

then add

Van De Walle, (1994)

Sample Problem: 3/5 + 1/2

Activity: Rectangle Dimensions

• Using the Dimensions of Rectangles Chart, use Cubes or Tiles to create as many rectangles as possible using the number of cubes listed in the left-hand column.

Table Numb

er

Numberof

cubes or tiles

Dimensions of Rectangles

Factors Prime or Composit

e?

1 132 123 234 245 296 77 88 119 9

10 1711 1812 27

• Using the Dimensions of Rectangles Chart, use Cubes or Tiles to create as many rectangles as possible using the number of cubes listed in the left-hand column.

• As students work with cubes or tiles they are making arrays. The use of arrays is a connection between previous years (3rd and 4th grade) and leads into more in-depth work that will follow in 6th grade.

• When students create the arrays using the tiles they determine the factors for the given number and define Composite or Prime.

Activity: Rectangle Dimensions

Table Number

Numberof cubes or tiles

Dimensions of Rectangles

Factors Prime or Composite?

1 13 1 by 13; 13 by 1 1, 13 Prime

2 12 1 by 12; 12 by 1; 2 by 6; 6 by 2; 3 by 4; 4 by 3

1, 2, 3, 4, 6, 12 Composite

3 23 1 by 23; 23 by 1 1, 23 Prime

4 24 1 by 24; 24 by 1; 2 by 12; 12 by 2; 3 by 8; 8 by 3; 4 by 6; 6 by 4

1, 2, 3, 4, 6, 8, 12, 24

Composite

5 29 1 by 29; 29 by 1 1, 29 Prime

6 7 1 by 7; 7 by 1 1, 7 Prime

7 8 1 by 8; 8 by 1; 2 by 4; 4 by 2 1, 2, 4, 8 Composite

8 11 1 by 11; 11 by 1 1, 11 Prime

9 9 1 by 9; 3 by 3; 9 by 1 1, 3, 9 Composite

10 17 1 by 17; 17 by 1 1, 17 Prime

11 18 1 by 18; 18 by 1; 2 by 9; 9 by 2; 3 by 6; 6 by 3

1, 2, 3, 6, 9, 18 Composite

12 27 1 by 27; 3 by 9; 9 by 3; 27 by 1 1, 3 , 9, 27 Composite

Measurement:

Materials: Number Generators, Recording Sheets Lesson Procedure: Begin the lesson with a review of area and perimeter concepts. Students will work in pairs to play the game “Rolling Rectangles”.Directions for the game:Roll two dice. Use the numbers as the dimensions (length and width) of a rectangle. Sketch the rectangle on grid paper and label the dimensions, area, and perimeter. Enter the area or perimeter of your rectangle as your “score” in one of the spaces on the recording sheet. If neither the area nor the perimeter will fit a category, enter it in the “CHANCE” space (if available) or enter a zero score in the space of your choice. Alternate rolls for 10 turns. If you are able to enter a score in all categories (not zero), score 10 extra points. Find the total points. Highest score wins!

Rolling Rectangles GameStandard of Learning 5.8

GeometryInstructional activity Place students into groups of three to four, and distribute straws, yarn, and number

cubes to each group. Demonstrate to students how the ends of straws must meet to form a triangle.

Thread a sample together and tie to create a triangle. Have the students toss three number generators and determine whether they can

form a triangle with straws whose lengths match the numbers thrown. If so, have them thread the three straws together with yarn or string and tie to form the triangle.

Distribute the recording sheet to students, and explain how to record results as they conduct the experiment. Tell them to wait to complete triangle-type section.

Instruct students to create as many possible triangles that they can in the allotted time.

After students have had time to conduct several trials, lead a classroom discussion on results.

Types of TrianglesStandard of Learning 5.12b

Probability and Statistics

How Much Are you Worth? We are going to make a human stem and leaf graph. Calculate the worth of their name if A=1, B=2, and so on.

Write the value of your name on a sheet of paper in large, dark print.

Tear the paper dividing the number between the ones and the tens.

On the floor there will be a stem-and-leaf graph using yarn. Come to the graph with your data. Arrange yourselves in order correctly on the graph. (from

least to greatest in the corresponding tens row)

Where do I stand?

• Stand next to the tens digit that would represent their data and hold the ones digit on the leaf side of the graph.

• For Example:– My name is Beth and my name is worth 35 points.

Stem (Tens)

Leaf(Ones)

0 tens

1 ten

2 tens

3 tens 35 (I would stand here)

4 tens

Organizing our Information

• Share conclusions …

– Describe your individual interpretations of the data.

• Next steps might include:

– drawing the stem and leaf plot and calculating the mean.

– asking the students to determine what the a typical person’s name is worth.

Where do I stand? Extension• Using the same stem and leaf plot that was

created in the “Where do I Stand?” activity lead students into “Describing the range, mean, mode, and median of the data?”

• Standard of Learning 5.16

Stem (Tens)

Leaf(Ones)

0 tens

1 ten

2 tens

3 tens 33 (I would stand here)

4 tens

Patterns, Functions, and Algebra

We know from studying multiplication tables that  5 × 12 = 60.  Look at the pictures and see how the same problem can be solved very easily!

= 5 X 10=50

5 X 2=10

5 X 12

5 x 12 = 5 × 10 = 50  +    5 × 2 = 10Each 12 is 10 + 2.  We multiply the tens and ones separately and then add:

5 × 12 = (5 × 10)  +  (5 × 2) = 50 + 10 = 60