THIRD GRADE MATHEMATICS
OVERVIEW OF ESSENTIAL SKILLS AND KNOWLEDGE
A student’s success in mathematics depends largely on the quality of the foundation that
is established during the first years of school.
A third grade mathematics program will:
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Develop conceptual understanding of number.
Involve children in doing mathematics.
Include concrete experiences, pictorial representations, and
abstract symbols.
Utilize problem-solving experiences.
Interpret the world using mathematics.
Include a broad range of content.
Provide appropriate use of technology.
As the year progresses, the student will:
Problem Solving – The student will use a variety of problem solving approaches to
ask and answer questions about mathematics and the real world.
♦ Ask questions about student’s own surroundings that can be solved using mathematics.
♦ Use problem-solving approaches, such as devise a plan, carry out the plan, and look
back, in order to answer such questions.
♦ Explain why answers make sense.
♦ Recognize irrelevant information in problem-solving situations.
Communication – The student will use a variety of techniques to communicate
mathematically.
♦ Express mathematical ideas to peers, teachers, and others.
♦ Agree or disagree with other students’ logic and processes and rephrase other students’
explanations.
♦ Use physical objects, pictures, diagrams, and symbols to express mathematical ideas.
♦ Relate everyday language to mathematical symbols and use appropriate mathematical
terminology.
Reasoning – The student will use a variety of mathematical reasoning skills to solve
problems.
♦ Identify and create patterns using physical objects, pictures,
and numbers.
♦ Demonstrate thinking processes using physical objects,
pictures, and explanations.
♦ Make predictions and draw conclusions about mathematical
ideas and concepts.
Connections – The student will make connections between
different aspects of mathematics, other disciplines, and the real
world.
♦ Use physical objects and pictures to represent concepts and
procedures (for example,
relate patterns on a hundreds chart to multiples).
♦ Make connections between concepts and symbols
(example: demonstrate 3 x 4 with a table consisting of 3 rows
and 4 columns).
♦ Recognize relationships among different topics within mathematics, such as the
relationship between multiplication and area of a geometric figure.
♦ Use mathematics to answer questions that arise in other subjects, such as science and
social studies, and in the real world.
Representation – The student will use a variety of representations to express data
and mathematical ideas.
♦ Use physical objects, pictures, and numbers to make charts, graphs, diagrams, tables,
and number sentences (example: 4 plus 7 is 11).
♦ Use charts, graphs, diagrams, tables, and number sentences to organize information and
answer questions about the real world.
Patterns and Algebraic Reasoning – The student will use a variety of problemsolving approaches to extend and create patterns.
♦ Describe, create, extend, and predict patterns using numbers.
♦ Analyze tables to formulate generalizations about patterns in a variety of situations
(example: when given a list of the first six multiples of 5, students should make the
generalization that all multiples of 5 end in 0 or 5).
Number Sense – The student will use numbers and number relationships to acquire
basic facts.
♦ Model the concept of place value through 4 digits using resources such as physical
objects, bundles of 10s, and place value mats.
♦ Read, model, and write whole numbers up to 4 digits.
♦ Compare and order whole numbers up to 4 digits.
♦ Compare and order fractions including halves, thirds, and fourths using physical
objects
and pictures.
Number Operations and Computation – The student will estimate and compute with
whole numbers.
♦ Estimate and find the sum and difference of 3-digit and 4-digit numbers to solve
application problems (example: An elementary school has 148 girls and 157 boys. How
many students are in the school all together?)
♦ Solve problems involving money that require addition and subtraction
(example: $20 – $14.96).
♦ Develop multiplication concepts (example: use physical objects to show 4 groups of 3
objects and explain multiplication as repeated addition).
♦ Memorize and apply multiplication facts and fact families.
7 x 8 = 56
56 ÷ 8 = 7
8 x 7 = 56
56 ÷ 7 = 8
♦ Estimate the product of 2-digit numbers by rounding to the
nearest multiple of 10 to solve application problems.
♦ Apply the commutative property of multiplication
(example:3 x 5 has the same valueas 5 x 3)
♦Apply the identity property of multiplication
(multiplying any number times 1 does not change its
value as demonstrated by 6 x 1 = 6).
♦ Use the associative property of addition
(example: when adding 3 + 2 + 1, a student can add 3 + 2 and then add 1, or the
student can add 2 + 1 and then add 3).
♦ Describe the inverse operation relationship between addition and subtraction.
♦ Complete addition number sentences with a missing addend, such as 3 + ? = 7.
Geometry and Measurement – The student will recognize and describe shapes and
use customary and metric measurements to solve problems.
♦ Describe and compare two- and three-dimensional shapes.
♦ Identify locations on a grid using ordered pairs, such as (D, 1) or (2, 3).
♦ Develop the concepts of perimeter and area.
♦ Estimate measurements.
♦ Solve problems involving length using half-inch, quarter-inch, meter, and centimeter.
♦ Solve problems involving weight using pound and ounce, and mass using gram and
kilogram.
♦ Tell time on digital and analog clocks t o 5 m i n u t e s, read a thermometer, and use
information to solve problems involving time and temperature.
Data Analysis – The student will demonstrate an understanding of data collection,
display and interpretation.
♦ Pose questions; collect, record, and interpret data to help answer questions.
♦ Read graphs and charts; identify the main idea, draw conclusions, make predictions
based on the data.
♦ Construct a bar graph or pictograph with labels and a title from a set of data.
♦ Describe the probability of chance events (for example, it is less likely to snow in May
than in January).
♦ List arrangements of up to three items (for example, possible ways to arrange three
scoops of chocolate, strawberry, and vanilla ice cream on a cone).
♦ List combinations of up to three items (for example, given the following table, list how
many different outfits can be made).