Download Patterns, Functions, and Relationships

3rd Grade Accelerated Blueprint-Level 1
Updated June 2012
1 of 7
Please Note—Changes related to the structure of the Teacher Blueprint Pages:
 To help teachers understand the groupings or clusters of standards, a topic name was provided
in, like "Equations and Expressions". This is followed by Essential Questions for the teacher and
the student to answer throughout the learning for that concept.
 The standards/performance objectives are sequenced within each topic.
 Multiple standards are located in the same row; these standards are intended to be taught in
tandem (concurrently) to maximize student learning and retention.
 At times, 2010 standards and 2008 standards are located in the same cell, indicating they are
tightly aligned. In these cases, it is important to teach the rigor of all standards in the same cell.
 Embedded Standards support teaching conceptually. These help students understand key
standards that will be taught in tandem throughout an entire topic. These are not Standards for
Mathematical Practice nor Process Integration Objectives, but are Content standards, like the
standards they are placed above
 Embedded Topics are topics that would not be assigned instructional time, but that are taught
during warm ups or in addition to another topic throughout a semester.
 While changes in the provided sequence are not intended, it is understood that changes may be
made to serve the needs of individual students.
3rd Grade Accelerated Blueprint-Level 1
Updated June 2012
2 of 7
Standards for Mathematical Practice
Standards
Explanations and Examples
Students are expected to:
3.MP.1. Make sense of
problems and persevere in
solving them.
3.MP.2. Reason abstractly and
quantitatively.
3.MP.3. Construct viable
arguments and critique the
reasoning of others.
3.MP.4. Model with
mathematics.
3.MP.5. Use appropriate tools
strategically.
3.MP.6. Attend to precision.
3.MP.7. Look for and make use
of structure.
3.MP.8. Look for and express
regularity in repeated reasoning.
In third grade, students know that doing mathematics involves solving problems and discussing how they solved them.
Students explain to themselves the meaning of a problem and look for ways to solve it. Third graders may use concrete
objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking
themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They
often will use another method to check their answers.
Third graders should recognize that a number represents a specific quantity. They connect the quantity to written
symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and
the meaning of quantities.
In third grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings.
They refine their mathematical communication skills as they participate in mathematical discussions involving questions
like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
Students experiment with representing problem situations in multiple ways including numbers, words (mathematical
language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students
need opportunities to connect the different representations and explain the connections. They should be able to use all
of these representations as needed. Third graders should evaluate their results in the context of the situation and
reflect on whether the results make sense.
Third graders consider the available tools (including estimation) when solving a mathematical problem and decide
when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have
a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all
the possible rectangles.
As third graders develop their mathematical communication skills, they try to use clear and precise language in their
discussions with others and in their own reasoning. They are careful about specifying units of measure and state the
meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers
in square units.
In third grade, students look closely to discover a pattern or structure. For instance, students use properties of
operations as strategies to multiply and divide (commutative and distributive properties).
Students in third grade should notice repetitive actions in computation and look for more shortcut methods. For
example, students may use the distributive property as a strategy for using products they know to solve products that
they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2
and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by
asking themselves, “Does this make sense?”
3rd Grade Accelerated Blueprint-Level 1
Updated June 2012
3 of 7
Patterns, Functions, and Relationships
Big Idea: Describe, identify, and model patterns, functions and their relationships. Apply pattern recognition to reason mathematically.
Essential Question Teacher: Can students apply patterns, functions, and their relationships within their mathematical reasoning?
Essential Question Student: Can I use patterns, functions, and their relationships to understand math problems?
Suggested Instructional Time: 2 Weeks
Strand Concept
Strand Concept
Strand Concept
S3C2PO 1. Recognize and describe a
relationship between two quantities, given by a
chart, table or graph, in which the quantities
change proportionally, using words, pictures,
or expressions.
The relationship can be given by a table, model, or
input/output (function) machine. In a function
relationship, each iteration should use the same
rule
Examples:

What rule is shown by the input/output
machine?
S3C1PO 1. Recognize, describe, extend,
create, and find missing terms in a
numerical sequence.
S3C1PO 2. Explain the rule for a given numerical sequence and verify that
the rule works.
Working with missing terms in sequences
provides an opportunity to reinforce addition,
subtraction, multiplication, and division facts.
Example:

What is the rule for the pattern?
2, 4, 6, 8, 10, …
o rule: add 2 to the previous
term
o verification: 2 + 2 = 4, 4 + 2
= 6, 6 + 2 = 8
Examples:

3, ___, 9, 12, 15, …

3
80, 72, 64, __, __, __, …
12
In
Out
1
4
2
8
3
12
4
16
The rule is x4 as each input is multiplied by 4 to get
the output value;
1 x 4 = 4, 2 x 4 = 8, 3 x 4 = 12, etc
What rule is shown by the function table?
X
Y
5
2
6
3
7
4
12
9
The rule is -3 as each value in column X is
subtracted by 3 to get the value in column Y.
Possible descriptions for the second pattern
include:

Each number is 8 less than the
previous number.
The first term is 8 x 10. The second is 8 x 9.
The 3rd term is 8 x 8. So, the next term must
be…
Resources
SF: Ch 1.9; 2.3; 5.4; 6.6-6.7; 6.10
NCTM Illuminations Lesson: Patterns that
Grow, Lesson 2
http://illuminations.nctm.org
MP. 2 Reason abstractly and
quantitatively.
MP. 7 Look for and make use
of structure.
MP. 8 Look for and express
regularity in repeated
reasoning.
Resources
SF: Ch 1.9; 2.3; 5.4; 6.6-6.7; 6.10
NCTM Illuminations Lesson: Patterns That
Grow, Lesson 2 http://illuminations.nctm.org
Continued on next page
3rd Grade Accelerated Blueprint-Level 1
Updated June 2012
4 of 7
Patterns, Functions, and Relationships
Big Idea: Describe, identify, and model patterns, functions and their relationships. Apply pattern recognition to reason mathematically.
Essential Question Teacher: Can students apply patterns, functions, and their relationships within their mathematical reasoning?
Essential Question Student: Can I use patterns, functions, and their relationships to understand math problems?
Suggested Instructional Time: 2 Weeks
Resources
SF: Ch. 6.10
S3C2PO 2. Translate
between the different
representations of
whole number
relationships,
including symbolic,
numerical, verbal, or
pictorial.
S3C3PO 2. Use a
symbol to represent
an unknown quantity
in a given context.
MP. 2 Reason abstractly and quantitatively.
Students can represent whole number functions using pictures, numbers,
symbols, and words.
MP. 4 Model with Mathematics

Pictures

Symbols
The number of points equals 5 x n (if n = the number of stars)

Words
Each
star has 5 points. In order to figure out the total number of points,
you multiply the number of stars by 5.

Table
MP. 5 Use tools strategically
(In Terms of Rules for
Patterns)
Stars

Number of Points
1
5
2
10
3
15
4
20
Chen baked 25 crackers. His friend ate some of the crackers. Chen
now has 9 crackers. 25 - ∆ = 9
Resources
SF: Ch. 5.2-4, Ch 1.6; 2.1-2.2; 2.4 Reading for Math Success pg. 268
TERC: Things That Come in Groups, Investigation 1
NCTM Illuminations Lesson: The Variable Machine http://illuminations.nctm.org
3rd Grade Accelerated Blueprint-Level 1
Updated June 2012
5 of 7
Algebraic Relationships
Big Idea: Represent and analyze mathematical situations and structures using algebraic representations
Essential Question Teacher: Can students make sense of algebraic representations?
Essential Question Student: Can I understand and prove algebraic equations?
Suggested Instructional Time: 2 Weeks
Strand Concept
S3C3PO 1. Record equivalent forms of whole numbers to
six digits by constructing models and using numbers.
Mathematical Practices
Strand Concept
MP. 2 Reason abstractly and
quantitatively.
Students may use manipulatives, pictures, or symbols to model whole
numbers and their equivalent forms.
MP. 7 Look for and make use of
structure.
Examples:





MP. 8 Look for and express regularity in
repeated reasoning.
142,350 = 100,000 + 40,000 + 2,000 + 300 + 50
3x8=6x4
3 x 8 = 15 + 9
20 = 10 + 5 + 5; 10 x 2; 10 + 10, 5 x 4; 10 + 10, etc.
Base Ten Model: 231
2 – 100’s; 3 –10’s +1 or
23 – 10’s + 1
Resources
SF: Ch 1.2-1.5
S3C3PO 2. Use a symbol to represent an unknown
quantity in a given context.
MP. 2 Reason abstractly and
quantitatively.
(In Terms of Algebraic Equations)
MP. 4 Model with Mathematics
S3C3PO 3. Create and solve simple one-step equations
that can be solved using addition and multiplication facts.
MP. 5 Use tools strategically
MP. 1 Make sense of problems and
persevere in solving them.
Students may create story problems or equations. When crafting story
problems, students should carefully consider the question(s) to be asked
and answered.
MP. 5 Use appropriate tools
3rd
Grade Accelerated Blueprint-Level 1
Updated June 2012
6 of 7
Algebraic Relationships
Big Idea: Represent and analyze mathematical situations and structures using algebraic representations
Essential Question Teacher: Can students make sense of algebraic representations?
Essential Question Student: Can I understand and prove algebraic equations?
Suggested Instructional Time: 2 Weeks
strategically.
Examples:

MP. 7 Look for and make use of
structure.
Solve the equations below:
5
x ∆ = 24
a x 2 x 2 = 24
78    92

Rachel has 3 bags. There are 4 marbles in each bag. How
many marbles does Rachel have altogether? 3 x 4 = m
Resources
SF: Ch 1.6; 2.1-2.2; 2.4
3rd Grade Accelerated Blueprint-Level 1
Updated June 2012
7 of 7