Title: Math
Grade Level(s): 3rd
Materials:
Objectives: Students will:
1. use mathematics to communicate, make connections, reason, and represent the world quantitatively in order to pose and solve
problems.
2. identify patterns on number grids.
3. compare and order numbers.
4. recognize and find equivalent names for a number.
5. use base-10 blocks and grids to represent decimal and fraction equivalencies.
6. calculate fractional parts of a region using base-10 blocks and grids.
7. utilize the number line as a model for fractions.
8. name quantities greater than 1 with fractions and mixed numbers.
9. write money amounts in dollar-and-cents notation.
10. identify the places in multi-digit numbers and the value of the digits in those places.
11. read, write, compare, and order whole numbers through the millions place.
12. identify and use number patterns to solve problems.
13. solve equations using algorithms.
14. estimate and compute accurately.
15. use estimation to determine whether the result of a computation is reasonable.
16. understand and explain the need for standard units of measurement.
17. measure line segments to the nearest inch, half inch, quarter inch, centimeter, half centimeter, and millimeter.
18. estimate and measure lengths using U.S. customary and metric units of length.
19. measure and calculate the perimeter of an object.
20. calculate the area of rectangles with the use of multiplication number models, arrays, and counting.
21. identify time to the nearest minute.
22. calculate elapsed time.
23. solve time and elapsed time number stories.
24. calculate the values of bills and coins.
25. solve problems involving money using a combination of coins and bills.
26. understand that everyday objects have a variety of attributes, each of which can be measured in many ways.
27. select and use appropriate standard units of measure and measurement tools to solve real-life problems.
28. use models and number facts to draw conclusions and explain reasons for conclusions.
29. apply mathematics in practical situations and in other disciplines.
30. solve problems that arise in mathematics and in other contexts: open-ended problems, non-routine problems, problems with multiple
solutions, problems that can be solved in several ways.
31. use the language of mathematics to express mathematical ideas precisely.
32. read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data; pictographs, bar graphs, line
plot graphs.
33. compare the data from two categories displayed in a graph.
34. compare representations of set data displayed in a graph.
35. determine the reasonableness of a statement based on a comparison to data displayed in a graph.
36. use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability.
37. determine whether different outcomes of the same event are likely, unlikely, certain, impossible, more likely, less likely, equally likely.
38. graph the possible results of an experiment.
39. determine that there can be a difference between predicted and actual outcomes.
40. represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts
and processes.
41. recognize, describe, extend, and create patterns.
42. represent number patterns and relationships by using variables.
43. apply multiple strategies to solve for unknown quantities.
44. use physical models to clarify mathematical relationships.
45. name, describe, and draw/build 2-and3-dimensional shapes.
46. will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze
phenomena.
47. identify and draw lines of symmetry.
48. use geometric principles to solve problems.
49. identify plotting coordinates on coordinate grids.
50. identify right angles in the environment.
Essential Questions:
1. How does understanding patterns, sequences, and functions help us to solve problems?
2. How can counting, measuring, or labeling help to make sense of the world around us?
3. What are efficient ways to count?
4. How can numbers be expressed, ordered, and compared?
5. How can we express equivalent forms of the same number by using concrete objects , drawings, word names, and symbols?
6. How can fractions be modeled, compared, and ordered?
7. How are common fractions and decimals alike and different?
8. How would we compare and order decimals through hundredths?
9. How does the position of a digit in a number affect its value?
10. How does understanding place value help us solve addition, subtraction, multiplication and division problems?
11. How are the four basic operations related to one another and what do they mean?
12. How does the use of mathematical strategies help us in the process of solving everyday problems?
13. How are repeated addition and multiplication related?
14. How are repeated subtraction, equal sharing, and forming equal groups used to solve division problems?
15. How does our knowledge about addition, subtraction, multiplication and division facts help us solve problems?
16. What strategies aid in mastering multiplication and division facts?
17. How do we decide which operation to use when solving mathematical problems?
18. How do we determine when to use an exact answer or when to use an estimate?
19. What strategies can we use to make a reasonable estimate?
20. In what ways do units of measure help us to quantify the world around us?
21. What tools and units are used to measure the attributes of an object?
22. How can measurements be used to solve problems?
23. What is the purpose of standard units of measurement?
24. How do units within a system relate to each other?
25. How can we measure volume, capacity, and weight?
26. What tools and units are used to measure the attributes of time?
27. How many different ways can specific amounts of money be made using various denominations of coins and bills?
28. What strategies can we use to estimate measurements?
29. Why is it important to give reasons to support mathematical conclusions and problem solutions?
30. Why is it necessary to interpret precise language in statements when solving problems?
31. How do we plan and apply problem-solving strategies to solve problems?
32. Why do we need to communicate mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in
writing?
33. Why are graphs helpful?
34. What data display is appropriate for a given set of data?
35. How can the collection, organization, interpretation, and display of data be used to answer questions?
36. How can experimental probabilities be used to make predictions or draw conclusions?
37. Where are patterns in nature, architecture, music, words, and numbers?
38. How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations?
39. Where in the real world can we find shapes, angles, and lines?
40. How can we identify and describe solid figures by describing the faces, edges, and sides?
41. How are points, lines, line segments, rays, and angles related?
42. How is the location of a point on a grid described?
Title: Numbers and Operations
Standards
Content (What the Student will Know)
Performance (What the Student will Do)
2.1.3.A
Count and Compare Numbers
Apply one-to-one correspondence and number
patterns to count up and count back and to compare
values of whole numbers and values of money.
2.1.3.B
2.1.3.C
CC.2.1.3.C.1
CC.2.3.3.A.2
Vocabulary
 number grid
 difference
 decimal point
 decimal
Represent Numbers in Equivalent Forms Represent equivalent forms of the same number
through the use of concrete objects, drawings, word
Vocabulary
names, and symbols.
 equivalent
 label
Concepts of Numbers and Relationships Use drawings, diagrams or models to show the concept
of fraction as part of a whole.
Vocabulary
Explain equivalence of fractions in special cases, and
 denominator
compare fractions by reasoning about their size.
 numerator
a. Understand two fractions as equivalent if they
 whole
are the same size, or the same point on a
 equivalent fractions
number line.
 mixed number
b. Recognize and generate simple equivalent
fractions, e.g. 1/2=2/4. Explain why the
Activities/Assessments
fractions are equivalent by using a visual
fraction model.
c. Express whole numbers as fractions, and
recognize fractions that are equivalent to whole
numbers. Examples:
Express 3=3/1, 1=4/4
Understand a fraction as a number on the number line;
represent fractions on a number line diagram.
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.
2.1.3.D
CC.2.1.3.B.1
2.1.3.E
Place Value
Vocabulary
 fact extension
 complements
 tenths
 hundredths
 thousandths
 decimeter
 digit
Number Theory
Vocabulary
 expanded form
 standard form
 even number
 odd number
Use the understanding of fractions to partition shapes
into parts with equal areas and express the area of
each part as a unit fraction of the whole.
Apply place-value concepts and base-ten numeration
to order and compare whole numbers.
Apply place-value understanding and properties of
operations to perform multi-digit arithmetic.
Multiply one-digit whole numbers by multiples of 10 in
the range 10-90 (e.g., 9x80, 5x60) using strategies
based on place value and properties of operations.
Apply number patterns even and odd, factors and
multiples to represent numbers in various ways.
2.1.3.F
Concepts and Applications of
Operations
Vocabulary
 fact family
 turn around rule
 parenthesis
2.2.3.A
CC.2.2.3.A.3
2.2.3.B
CC.2.2.3.A.1
CC.2.2.3.A.2
2.2.3.D
Fluency in Basic Facts
Vocabulary
 square numbers
 multiples
Computation
Vocabulary
 algorithm
 addend
 multiplication
 array
 factor
 product
 division
 quotient
 dividend
 divisor
 remainder
 sum
Numerical Estimation
Vocabulary
 estimate
 ballpark
Understand the concepts of addition and subtraction
and use the inverse relationships between addition and
subtraction to determine unknown quantities in
equations.
Identify arithmetic patterns (including patterns in the
addition table or multiplication table), and explain
them using properties of operations.
Develop fluency in the use of basic facts for the four
operations.
Demonstrate multiplication and division fluency.
Add and subtract single-and double-digit numbers with
regrouping and
triple-digit numbers, without regrouping including
problems with money.
Represent and solve problems involving multiplication
and division.
Understand properties of multiplication and the
relationship between multiplication and division.
Estimate values, sum, and differences of quantities and
conclude the reasonableness of those estimates.
Rounding numbers to the nearest 10 or 100.
2.3.3.A
 estimate
 rounding
Concept of Measurement
2.3.3.B
Units and Tools of Measurement
2.3.3.C
Vocabulary
 inch
 yard
 centimeter
 millimeter
 standard unit
 foot
 U.S. customary system
 metric system
 Fahrenheit scale
 Celsius scale
Calculations
Vocabulary
 calculate
 elapsed time
 a.m.
 p.m.
2.3.3.D
CC.2.4.3.A.2
2.3.3.F
CC.2.4.3.A.1
Conversions
Measurement Estimation
Vocabulary
 length
Demonstrate an understanding of measurable
characteristics and the need to quantify those
characteristics.
Identify a measurable characteristic of an object, select
an appropriate standard or non-standard unit of
measure and tool, and determine the measurement to
a specified level of accuracy.
Tell time on an analog and digital clock to the nearest
minute and measure time intervals in minutes, identify
times of day and night as a.m. and p.m., and calculate
elapsed time.
Solve word problems involving addition and
subtraction of time intervals in minutes, e.g., by
representing the problem on a number line diagram.
Identify equivalent measurements within the same
system.
Solve problems involving money using a combination of
coins and bills.
Estimate and verify measurements of length, area,
weight, and capacity.
2.4.3.A
 weight
 capacity
 volume
 mass
 grams
 kilograms
 liter
 map scales
Reasoning
2.4.3.B
Vocabulary
 number
 model
 unit
 number sentence
Connections
2.5.3.A
CC.2.2.3.A.4
Problem Solving
2.5.3.B
Communication
2.6.3.A
Collection of Data
2.6.3.B
CC.2.4.3.A.4
Organization and Display of Data
Vocabulary
 scale
 bar graph
 line plot
Measure and estimate liquid volumes and masses of
objects using standard units of grams (g), kilograms
(kg), and liters (l). 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
drawing (such as a beaker with a measurement scale)
to represent the problem.
Use models and number facts to draw conclusions and
explain reasons for conclusions.
Interpret statements made with precise language of
logic
(e.g., all, or every, none, some, or many)
Develop a plan to analyze two step problems using the
four operations, identify the information needed to
solve the problem, carry out the plan, check whether
an answer makes sense using mental computation and
estimation strategies, and explain how the problem
was solved in grade appropriate texts.
Use appropriate mathematical vocabulary when
explaining how to solve a problem.
Gather data from surveys and observations within the
classroom or homes.
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.
2.6.3.C
Numerical Summaries
2.6.3.D
Vocabulary
 line graph
 pie graph
 tally chart
Statistical Comparisons
2.6.3.E
Vocabulary
 minimum
 maximum
 range
 mode
 median
 average
Interpretation of Data
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.
Describe data displayed in a diagram (e.g., Venn) a
graph or a table.
Analyze data shown in tables, charts, diagrams, and
graphs; compare the data from two categories
displayed in a graph and compare representations of a
set of data in different graphs.
Determine the reasonableness of a statement based on
a comparison to data displayed in a graph.
Title: Algebra Concepts
Standards
Content (What the Student will Know)
Performance (What the Student will Do)
2.7.3.A
Calculation of Probabilities
2.7.3.B
Vocabulary
 event
 probability
Prediction of Outcomes
Determine the chance of an event occurring by
performing simulations with concrete devices (e.g.,
dice, spinner)
2.7.3.C
2.7.3.D
2.7.3.E
2.8.3.A
Representations of Probabilities
Display Simple Spaces
Compare Theoretical and Experimental
Probabilities
Algebraic Properties
2.8.3.B
Algebraic Manipulations
2.8.3.C
Patterns
2.8.3.D
Functions
2.8.3.E
Vocabulary
 function
 machine
 rule
 input
 output
Modeling
2.8.3.F
Interpret Results of Modeling
Determine whether different outcomes of the same
event are equally likely or not equally likely.
Write the likelihood of an event as a fraction.
List or graph the possible results of an experiment.
Determine that there can be a difference between
predicted and actual outcomes.
Use the concept of equality and concrete objects to
demonstrate understanding of commutative,
associative, and identity properties.
Use concrete objects and trial and error to solve
number sentences (equations and inequalities)
Recognize, describe, extend, create, and replicate a
variety of patterns including attribute, activity, number,
and geometric patterns.
Use a rule to find a missing value and determine a rule
for a given pattern.
Use concrete objects or combinations of symbols and
numbers to represent expressions, equations, and
inequalities that model mathematical situations.
Describe data represented in a table, chart, or number
sentence and/or create a story that matches that data.
Activities/Assessments
2.9.3.A
CC.2.3.3.A.1
CC.2.4.3.A.5
CC.2.4.3.A.6
Definitions, Properties, and Relations
Vocabulary
 attribute
 ray
 line segment
 line
 endpoint
 triangle
 3 dimensional shapes
 2 dimensional shapes
 square
 rhombus
 rectangle
 parallelogram
 trapezoid
 polygon
 quadrilateral
 perimeter
 area
 tiling
 square feet
 square yards
 circumference
 diameter
 parallel
 intersect
 quadrangle
 kite
 plane figure
 congruent
 pyramid
 triangular prism
 rectangular prism
 hexagonal prism
Name and describe and draw/build 2-and 3dimensional shapes.
Understand that shapes in different categories (e.g.,
rhombuses, rectangles, and others) may share
attributes (e.g., having four sides), and that the shared
attributes can define a larger category (e.g.,
quadrilaterals). Recognize rhombuses, rectangles, and
squares as examples of quadrilaterals, and draw
examples of quadrilaterals that do not belong to any of
these subcategories.
Solve real world and mathematical problems involving
perimeters of polygons, including finding the perimeter
given the side lengths, finding an unknown side length,
and exhibiting rectangles with the same perimeter and
different areas or with the same area and different
perimeters.
Determine the area of a rectangle and apply the
concept to multiplication and to addition. Recognize
area as an attribute of plane figures.
2.9.3.B
 cone
 cylinder
 sphere
 apex
 polyhedron
 face
 edge
 base
Transformations and Symmetry
2.9.3.C
Vocabulary
 symmetric
 symmetry
 line of symmetry
 translation
Coordinate Geometry
2.10.3.A
Vocabulary
 ordered pair
 coordinates
 coordinate grid
Right Triangle Concepts and
Applications
2.11.3.A
Vocabulary
 vertex
 vertices
 right angle
 equilateral triangle
 degree
 turn
Extreme Values
CC.2.1.3.C.1
Fractions
Identify and draw lines of symmetry.
Identify locations of points with whole number
coordinates on a number line or on a 2-dimensional
coordinate system.
Identify right angles in the environment
Identify whole number quantities and measurements
from least to most and greatest value.
Explore and develop an understanding of fractions as
numbers.