5th Grade GSO Math

Educational Technology Center

By the end of grade five, students will further develop their understanding of multiplication and division of whole numbers and decimal fractions. They will also understand and investigate algebraic mathematical expressions. Students will also expand their understanding of computing area and volume of simple geometric figures. Students will understand the meaning of congruent geometric shapes and the relationship of the circumference of a circle to its diameter. They will also use percentages and circle graphs to interpret statistical data.
Instruction and assessment should include the use of manipulatives and appropriate technology. Topics should be represented in multiple ways including concrete/pictorial, verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be introduced and used in the context of real world phenomena.

 

Concepts/Skills to Maintain
Add and subtract decimal fractions
Whole numbers and decimal fraction
computation
Angle measurement
Length, area, and weight
Number sense
Add and subtract common fractions with
like denominators
Data usage and representation
Characteristics of 2D and 3D shapes
Order of Operations


NUMBER AND OPERATIONS
Students will further develop their understanding of the concept of whole numbers. They will also understand the meanings of multiplication and division of decimal fractions and use decimal fractions and common fractions in computation, as well as in problem solving situations.

M5N1. Students will further develop their understanding of whole numbers.

a. Classify the set of counting numbers into subsets with distinguishing
characteristics (odd/even, prime/composite).
b. Find multiples and factors.
c. Analyze and use divisibility rules.

M5N2. Students will further develop their understanding of decimal fractions as part of the base-ten number system.

a. Understand place value.
b. Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, and 0.01.

M5N3. Students will further develop their understanding of the meaning of multiplication and division with decimal fractions and use them.

a. Model multiplication and division of decimal fractions by another decimal fraction.
b. Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimal fractions.
c. Multiply and divide with decimal fractions including decimal fractions less than one and greater than one.
d. Understand the relationships and rules for multiplication and division of whole numbers also apply to decimal fractions.

M5N4. Students will continue to develop their understanding of the meaning of common fractions and compute with them.

a. Understand division of whole numbers can be represented as a fraction (a/b= a ÷ b).
b. Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one.
c. Find equivalent fractions and simplify fractions.
d. Model the multiplication and division of common fractions.
e. Explore finding common denominators using concrete, pictorial, and
computational models.
f. Use <, >, or = to compare fractions and justify the comparison.
g. Add and subtract common fractions and mixed numbers with unlike
denominators.
h. Use fractions (proper and improper) and decimal fractions interchangeably.
i. Estimate products and quotients.

M5N5. Students will understand the meaning of percentage.

a. Model percent on 10 by 10 grids.
b. Apply percentage to circle graphs.


MEASUREMENT
Students will compute the area of geometric plane figures. They will also understand the concept of volume and compute the volume of simple geometric solids and measure capacity. Students will convert from one unit to another within one system of measurement.
M5M1. Students will extend their understanding of area of fundamental geometric
plane figures
.

a. Estimate the area of fundamental geometric plane figures.
b. Derive the formula for the area of a parallelogram (e.g., cut the
parallelogram apart and rearrange it into a rectangle of the same area).
c. Derive the formula for the area of a triangle (e.g. demonstrate and explain its
relationship to the area of a rectangle with the same base and height).
d. Find the areas of triangles and parallelograms using formulae.
e. Estimate the area of a circle through partitioning and tiling and then with formula (let pi = 3.14). (Discuss square units as they apply to circles.)
f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.

M5M3. Students will measure capacity with appropriately chosen units and tools.

a. Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to
measure capacity.
b. Compare one unit to another within a single system of measurement (e.g., 1 quart = 2 pints).

M5M4. Students will understand and compute the volume of a simple geometric solid.

a. Understand a cubic unit (u3) is represented by a cube in which each edge has the length of 1 unit.
b. Identify the units used in computing volume as cubic centimeters (cm3),
cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3).
c. Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.
d. Compute the volume of a cube and a rectangular prism using formulae.
e. Estimate the volume of a simple geometric solid.
f. Understand the similarities and differences between volume and capacity.


GEOMETRY
Students will further develop their understanding of geometric figures.

M5G1. Students will understand congruence of geometric figures and thecorrespondence of their vertices, sides, and angles.
 

M5G2. Students will understand the relationship of the circumference of a circle toits diameter is pi (π ≈ 3.14).


ALGEBRA
Students will represent and investigate mathematical expressions algebraically by using variables.
M5A1. Students will represent and interpret the relationships between quantities algebraically.

a. Use variables, such as n or x, for unknown quantities in algebraic
expressions.
b. Investigate simple algebraic expressions by substituting numbers for the unknown.
c. Determine that a formula will be reliable regardless of the type of number (whole numbers or decimal fractions) substituted for the variable.

DATA ANALYSIS
Students will gather, organize, and display data and interpret graphs.
M5D1. Students will analyze graphs.

a. Analyze data presented in a graph.
b. Compare and contrast multiple graphic representations (circle graphs, line graphs, bar graphs, etc.) for a single set of data and discuss the advantages/disadvantages of each.

M5D2. Students will collect, organize, and display data using the most appropriate graph.