Transcript Grade 5

Virginia Mathematics
2009 Grade 5 Standards of Learning
Virginia Department of Education
K-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 bullets
EX:
(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 Changes
Details on instructional strategies have been
removed for potential placement in the Curriculum
Framework
EX:
(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
Sample Problem: 3/5 + 1/2
Van De Walle, (1994)
Sample Problem: 3/5 + 1/2
3/5
=
6/10
+
+
1/2
=
Van De Walle, (1994)
5/10
Sample Problem: 3/5 + 1/2
3/5
=
6/10
Rewrite
6/10 +
5/10
+
+
1/2
=
then add
5/10
Van De Walle, (1994)
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
Number
Number of cubes
or tiles
1
2
13
12
3
4
5
6
23
24
29
7
7
8
9
8
11
9
10
11
17
18
12
27
Dimensions of
Rectangles
Factors
Prime or
Composite?
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.
• 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.
Table
Number
Number
of 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
Rolling Rectangles Game
Standard of Learning 5.8
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!
Types of Triangles
Geometry
Standard of Learning 5.12b
 Instructional 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.
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
4 tens
35 (I would stand here)
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
4 tens
33 (I would stand here)
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 = 10
Each 12 is 10 + 2. We multiply the tens and
ones separately and then add:
5 × 12 = (5 × 10) + (5 × 2) = 50 + 10 = 60