The California Mathematics Content Standards

The symbol
identifies the key
standards for
grade five.

1.0 Students compute with very large and very small numbers, positive integers,
decimals, and fractions and understand the relationship between decimals,
fractions, and percents. They understand the relative magnitudes of numbers:

1.1 Estimate, round, and manipulate very large (e.g., millions) and very small
(e.g., thousandths) numbers.

Interpret percents as a part of a hundred; find decimal and percent equivalents
for common fractions and explain why they represent the same value;
compute a given percent of a whole number.

A test had 48 problems. Joe got 42 correct.

1. What percent were correct?

2. What percent were wrong?

3. If Moe got 93.75% correct, how many problems did he get correct?

1.3 Understand and compute positive integer powers of nonnegative integers;
compute examples as repeated multiplication.

Extend the tables shown below:

Determine the prime factors of all numbers through 50 and write the
numbers as the product of their prime factors by using exponents to show
multiples of a factor (e.g., 24 = 2 × 2 × 2 × 3 = 2³ × 3).

Find the prime factorization of 48 and use exponents where appropriate.

Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.

2.0 Students perform calculations and solve problems involving addition, subtraction,
and simple multiplication and division of fractions and decimals:

Add, subtract, multiply, and divide with decimals; add with negative
integers; subtract positive integers from negative integers; and verify the
reasonableness of the results.

Determine the following numbers:

1. 11 + (-23)

2. (-15) - 128

3. (-27) + (-45)

Demonstrate proficiency with division, including division with positive
decimals and long division with multidigit divisors.

Find the quotient:

6 divided by .025

Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers ( like and
unlike denominators of 20 or less ), and express answers in the simplest form.

Given the following three pairs of fractions (3/8 and 1/6, and , 16 and
), find for each pair its:

1. Sum

2. Difference

2.4 Understand the concept of multiplication and division of fractions.

2.5 Compute and perform simple multiplication and division of fractions and
apply these procedures to solving problems.

Given the following three pairs of fractions (3/8 and 1/6, and , 16 and
), find for each pair its:

1. Product

2. Quotient in simplest terms

Ericka has yards of cloth to make shirts. Each shirt requires 7/8 yard.
How many shirts can she make? How much cloth will she have left over?
 

Use a letter to represent an unknown number ; write and evaluate simple
algebraic expressions in one variable by substitution.

3x + 2 = 14. What is x?

1.3 Know and use the distributive property in equations and expressions with
variables.

Identify and graph ordered pairs in the four quadrants of the coordinate
plane.

Plot the points (1, 2), (-4, -3), (12, -1), (0, 4), (-4, 0).

Solve problems involving linear functions with integer values; write the
equation ; and graph the resulting ordered pairs of integers on a grid.
 

Derive and use the formula for the area of a triangle and of a parallelogram
by comparing it with the formula for the area of a rectangle (i.e., two of the
same triangles make a parallelogram with twice the area; a parallelogram is
compared with a rectangle of the same area by pasting and cutting a right
triangle on the parallelogram).

Find the area and perimeter.

Construct a cube and rectangular box from two-dimensional patterns and
use these patterns to compute the surface area for these objects.

Understand the concept of volume and use the appropriate units in common
measuring systems (i.e., cubic centimeter [cm ³], cubic meter [m³], cubic
inch [in. ³], cubic yard [yd.³]) to compute the volume of rectangular solids.

1.4 Differentiate between , and use appropriate units of measures for, two- and
three-dimensional objects (i.e., find the perimeter, area, volume).

2.0 Students identify, describe, and classify the properties of, and the relationships
between, plane and solid geometric figures:

Measure, identify, and draw angles, perpendicular and parallel lines,
rectangles, and triangles by using appropriate tools (e.g., straightedge,
ruler, compass, protractor, drawing software).

Know that the sum of the angles of any triangle is 180° and the sum
of the angles of any quadrilateral is 360° and use this information to solve
problems.

2.3 Visualize and draw two-dimensional views of three-dimensional objects
made from rectangular solids.
 

Identify ordered pairs of data from a graph and interpret the meaning of the
data in terms of the situation depicted by the graph.

Know how to write ordered pairs correctly; for example, (x, y).