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.
Standards for Mathematical PracticeStandards / Explanations and Examples
Students are expected to:
3.MP.1. Make sense of problems and persevere in solving them. / 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.
3.MP.2. Reason abstractly and quantitatively. / 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.
3.MP.3. Construct viable arguments and critique the reasoning of others. / 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.
3.MP.4. Model with mathematics. / 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.
3.MP.5. Use appropriate tools strategically. / 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.
3.MP.6. Attend to precision. / 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.
3.MP.7. Look for and make use of structure. / 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).
3.MP.8. Look for and express regularity in repeated reasoning. / 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?”
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 ConceptS3C2PO 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. / 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.
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?
In Out
14
28
312
416
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.
Continued on next page
Resources
SF: Ch. 6.10 / Working with missing terms in sequences provides an opportunity to reinforce addition, subtraction, multiplication, and division facts.
Examples:
- 3, ___, 9, 12, 15, …
- 80, 72, 64, __, __, __, …
- Each number is 8 less than the previous number.
Resources
SF: Ch 1.9; 2.3; 5.4; 6.6-6.7; 6.10
NCTM Illuminations Lesson: Patterns That Grow, Lesson 2 / Example:
- What is the rule for the pattern?
- rule: add 2 to the previous term
- verification: 2 + 2 = 4, 4 + 2 = 6, 6 + 2 = 8
SF: Ch 1.9; 2.3; 5.4; 6.6-6.7; 6.10
NCTM Illuminations Lesson: Patterns that Grow, Lesson 2
/ 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.
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.
(In Terms of Rules for Patterns) / MP. 2 Reason abstractly and quantitatively.
MP. 4 Model with Mathematics
MP. 5 Use tools strategically / Students can represent whole number functions using pictures, numbers, symbols, and words.
- 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
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
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
Algebraic Relationships
Big Idea: Represent and analyze mathematical situations and structures using algebraic representationsEssential 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 / Mathematical Practices / Strand ConceptS3C3PO 1. Record equivalent forms of whole numbers to six digits by constructing models and using numbers. / 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. / Students may use manipulatives, pictures, or symbols to model whole numbers and their equivalent forms.
Examples:
- 142,350 = 100,000 + 40,000 + 2,000 + 300 + 50
- 3 x 8 = 6 x 4
- 3 x 8 = 15 + 9
- 20 = 10 + 5 + 5; 10 x 2; 10 + 10, 5 x 4; 10 + 10, etc.
- Base Ten Model: 231
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.
(In Terms of Algebraic Equations) / MP. 2 Reason abstractly and quantitatively.
MP. 4 Model with Mathematics
MP. 5 Use tools strategically
S3C3PO 3. Create and solve simple one-step equations that can be solved using addition and multiplication facts. / MP. 1 Make sense of problems and persevere in solving them.
MP. 5 Use appropriate tools strategically.
MP. 7 Look for and make use of structure. / Students may create story problems or equations. When crafting story problems, students should carefully consider the question(s) to be asked and answered.
Examples:
- Solve the equations below:
a x 2 x 2 = 24
- Rachel has 3 bags. There are 4 marbles in each bag. How many marbles does Rachel have altogether? 3 x 4 = m
SF: Ch 1.6; 2.1-2.2; 2.4
3rd Grade Accelerated Blueprint-Level 11 of 7
Updated June 2012