2015-2016 3rd Grade 4th Quarter Mathematics Scope and Sequence
Unifying Concept: Operations and Geometry
Mathematics Content Focus:
Mathematical Practice Focus
Students solve problems involving the four operations Mathematically Proficient Students…
and continue to use place value understanding and
3. Construct viable arguments and critique the reasoning
properties of operations to perform multi-digit
of others.
arithmetic.
4. Model with mathematics.
Students develop their understanding of
6. Attend to precision.
measurement topics to solve problems and to
7. Look for and make use of structure.
estimate quantities.
Target Standards
3.OA.C.7F
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.
3.OA.D.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. (Note: This standard is
limited to problems posed with whole numbers and having whole-number answers; students should
know how to perform operations in the conventional order when there are no parentheses to
specify a particular order -- Order of Operations.)
3.NBT.A.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.MD.A.2
Measure and estimate liquid volumes and masses of objects using standard units of grams (g),
kilograms (kg), and liters (l). (Note: Excludes compound units such as cm3 and finding the
geometric volume of a container.) 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. (Note: Excludes
multiplicative comparison problems -- problems involving notions of “times as much”; see Glossary,
Table 2.)
3.MD.B.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.
3.MD.B.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.
Quarter Major Clusters
Arizona considers Major Clusters as groups of related standards that require greater emphasis than some of the
others due to the depth of the ideas and the time it takes to master these groups of related standards.
3.OA.C Multiply and divide within 100
Essential Concepts
Essential Questions
 The foundation for fluency is based on the study
 What strategies help you solve an unknown fact?
of patterns and relationships in multiplication and
o How can you use known facts to help you find
division facts.
unknown facts? If you don’t know 6x9, how can
you use 6x10 to help?
 How can you explain the patterns observed in
multiplication and division combinations/facts?
3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic
Essential Concepts:
Essential Questions:
 The four basic arithmetic operations are
 How are addition, subtraction, multiplication and
interrelated, and the properties of each may be
division related?
used to understand the others.
 What strategies help you determine the
 Some mathematical problems may require
reasonableness of an answer?
multiple steps to solve.
 What numeric patterns do you see? Use the
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Curriculum Instruction and Professional Development Math Department
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2015-2016 3rd Grade 4th Quarter Mathematics Scope and Sequence
properties of operation(s) to explain why those
 Unknowns in an equation can be represented by a
patterns exist.
letter or symbol (a or b rather than ∆ or ).

How can estimation be useful when solving
 Estimation can be used to determine the
multiplication and division problems?
reasonableness of an answer.
3.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic
Essential Concepts:
Essential Questions:
 Place value is essential to developing number
 How can the patterns of multiples of 10 help you solve
sense and multiple efficient strategies for
problems?
computing with numbers.
 How does place value help you estimate?
 There are patterns when multiplying by multiples
 How do halfway points help you round?
of 10.
 How are estimating and rounding similar to and
 Place value understanding is the foundation for
different from each other?
being able to estimate and round numbers.
3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and
masses of objects
Essential Concepts:
Essential Questions:
 Standardized measurement is used to describe
 Why does “what” we measure influence “how” we
and quantify the world.
measure?
 Elapsed time is a measure of the duration of an
 What units and tools are used to measure
event. It can be determined using addition and/or
o How long it takes to get to school in the morning?
subtraction on a number line.
o How much water you drink in one day?
o Which is heavier, e.g., a pencil or a calculator?
 Liquid volume measures the amount of liquid (or
other pourable substance) a container can hold. It  Estimate and then measure the liquid volume of this
can be measured with metric units such as liters
container. Why did you choose that tool? How close
and milliliters.
was your estimate?
 Mass is the amount of matter in an object and, on  What is the relationship between grams and
Earth, is measured in the same way as weight.
kilograms? Give an example that illustrates the
convenience of this relationship.
 Mass can be measured using metric units such as
grams and kilograms.
 What is the relationship between liters and milliliters?
How does knowing this relationship help to measure?
 Benchmark measurements help to develop an
understanding of incremental units and increases
familiarity with units, e.g., a large plastic bottle of
soda is 2 liters.
3.MD.B Represent and interpret data
Essential Concepts:
Essential Questions:
 Data can be collected and represented in many
 How can you represent your data in a way that makes
ways, including graphs or line plots.
sense?
 The foundation of a line plot is a number line; an
 How are the parts of a graph helpful to a reader? What
‘X’ is made above the corresponding value using
might be the result of not having those parts?
whole and mixed number (halves and fourths)
 What comparison problems can you create from your
units on the line for every corresponding piece of
data?
data.
 Why do intervals need to be in equal increments?
 Labeling graphs or line plots helps to interpret the
representation.
 Graphs can be read to compare and contrast
information.
 Scaled intervals are important for accurate graph
representations.
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Curriculum Instruction and Professional Development Math Department
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