Third Grade California Common Core Standards: Math
CALIFORNIA COMMON CORE STANDARDS: MATH
GRADE 3
3.OA: OPERATIONS AND ALGEBRAIC THINKING
Represent and solve problems involving multiplication and division.
1. Interpret products of whole numbers, e.g., interpret 5 × 7 as
the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects
can be expressed as 5 × 7.
2. Interpret whole-number quotients of whole numbers, e.g.,
interpret 56 ÷ 8 as the number of objects in each share when
56 objects are partitioned equally into 8 shares, or as a
number of shares when 56 objects are partitioned into equal
shares of 8 objects each. For example, describe a context in
which a number of shares or a number of groups can be
expressed as 56÷8.
3. Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and
equations with a symbol for the unknown number to
represent the problem.
4. Determine the unknown whole number in a multiplication or
division equation relating three whole numbers. For example,
determine the unknown number that makes the equation true
Understand properties of multiplication and the relationship between multiplication and division.
5.Apply properties of operations as strategies to multiply and
divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is
also known. (Commutative property of multiplication.) 3 × 5 × 2
can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.)
Knowing that 8 × = 40 and 8 × 2 = 16, one can find 8 × 7 as 8
× (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property.)
6. Understand division as an unknown-factor problem. For
example, find 32 ÷ 8 by finding the number that makes
32 when multiplied by 8.
Multiply and divide within 100.
7. Fluently multiply and divide within 100, using strategies such
as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of
operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
8. Solve two-step word problems using the four operations.
Represent these problems using equations with a letter
standing for the unknown quantity. Assess the reasonableness
of answers using mental computation and estimation
strategies including rounding.
9. Identify arithmetic patterns (including patterns in the addition
table or multiplication table), and explain them using properties
of operations. For example, observe that 4 times a number is
always even, and explain why 4 times a number can be
decomposed into two equal addends.
3.NBT: NUMBER AND OPERATIONS IN BASE TEN
Use place value understanding and properties of operations to perform multi-digit arithmetic.
1.Use place value understanding to round whole numbers
to the nearest 10 or 100.
2. Fluently add and subtract within 1000 using strategies and
algorithms based on place value, properties of operations,
and/or the relationship between addition and subtraction.
3. Multiply one-digit whole numbers by multiples of 10 in the
range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on
place value and properties of operations.
3.NF: NUMBER AND OPERATIONS-FRACTIONS
Develop understanding of fractions as numbers.
1. Understand a fraction 1/b as the quantity formed by 1 part
when a whole is partitioned into b equal parts; understand a
fraction a/b as the quantity formed by a parts of size 1/b.
2. Understand a fraction as a number on the number line;
represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by
defining the interval from 0 to 1 as the whole and
partitioning it into b equal parts. Recognize that each
part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by
marking off a lengths 1/b from 0. Recognize that the
resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
3. Explain equivalence of fractions in special cases, and compare
fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are
the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are
equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
d. Compare two fractions with the same numerator or the
same denominator by reasoning about their size.
Recognize that comparisons are valid only when the two
fractions refer to the same whole. Record the results of
comparisons with the symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
3.MD: MEASUREMENT AND DATA
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
1.Tell and write time to the nearest minute and measure time
intervals in minutes. Solve word problems involving addition
and subtraction of time intervals in minutes, e.g., by
representing the problem on a number line diagram.
2.Measure and estimate liquid volumes and masses of objects
using standard units of grams (g), kilograms (kg), and liters
(l).6 Add, subtract, multiply, or divide to solve one-step word
problems involving masses or volumes that are given in the
same units, e.g., by using drawings (such as a beaker with a
measurement scale) to represent the problem.
Represent and interpret data.
3. Draw a scaled picture graph and a scaled bar graph to
represent a data set with several categories. Solve one- and
two-step "how many more" and "how many less" problems
using information presented in scaled bar graphs. For
example, draw a bar graph in which each square in the bar
graph might represent 5 pets.
4. Generate measurement data by measuring lengths using
rulers marked with halves and fourths of an inch. Show the
data by making a line plot, where the horizontal scale is
marked off in appropriate units— whole numbers, halves, or
quarters.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
5. Recognize area as an attribute of plane figures and
understand concepts of area measurement.
a. A square with side length 1 unit, called "a unit square," is
said to have "one square unit" of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or
overlaps by n unit squares is said to have an area of n
square units.
6. Measure areas by counting unit squares (square cm, square
m square in, square ft., and improvised units).
7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side
lengths by tiling it, and show that the area is the same as
would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a
rectangle with whole-number side lengths a and b + c is
the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear
figures by decomposing them into non-overlapping
rectangles and adding the areas of the non- overlapping
parts, applying this technique to solve real world problems.