Grade 3 Accelerated Mathematics (#5012055) 

Clarification 2: Within the benchmark, the expectation is to utilize parentheses. 

Clarification 3: Multiplication for products of three or more numbers is limited to factors within 12. Refer to Properties of Operations, Equality and Inequality (Appendix D).

Clarification 2: Multiplication is limited to factors within 12 and related division facts. Refer to Situations Involving Operations with Numbers (Appendix A).

Clarification 2: Within this benchmark, the symbolic representation of the missing factor uses any symbol or a letter.

Clarification 2: Problem types are limited to an equation with three or four terms. The product or quotient can be on either side of the equal sign. 

Clarification 3: Multiplication is limited to factors within 12 and related division facts.

Clarification 2: Problem types include patterns involving addition, subtraction, multiplication or division of whole numbers.

 Clarification 2: Instruction includes the connection between multiplication and the number of data points represented by a bar in scaled bar graph or a scaled column in a pictograph.

Clarification 3: Data displays are represented both horizontally and vertically.

 Clarification 2: Data displays can be represented both horizontally and vertically.

Clarification 3: Circle graphs are limited to showing the total values in each category.

Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12.

Clarification 2: Denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12.

Clarification 2: Denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12.

Clarification 3: Fractions include fractions greater than one, including mixed numbers, with denominators limited to 2, 3, 4, 5, 6, 8, 10 and 12.

Clarification 2: Within this benchmark, the expectation is not to generate equivalent fractions. 

Clarification 3: Fractions are limited to fractions less than or equal to one with denominators of 2, 3, 4, 5, 6, 8, 10 and 12. Number lines must be given and scaled appropriately.

Example: The fractions and can be identified as not equivalent using a visual model.

Clarification 2: When working with perpendicular lines, right angles can be called square angles or square corners.

Clarification 2: Quadrilaterals will be filled, outlined or both when identifying.

Clarification 3: Drawing representations must be reasonably accurate.

Clarification 2: Instruction includes folding paper along a line of symmetry so that both halves match exactly to confirm line-symmetric figures.

Clarification 2: Two-dimensional figures cannot exceed 12 units by 12 units and responses include the appropriate units in word form (e.g., square centimeter or sq.cm.).

Clarification 2: Two-dimensional figures cannot exceed 12 units by 12 units and responses include the appropriate units in word form.

Clarification 2: Two-dimensional figures cannot exceed 12 units by 12 units and responses include the appropriate units in word form.

Clarification 2: Each rectangle within the composite figure cannot exceed 12 units by 12 units and responses include the appropriate units in word form.

Clarification 2: When measuring the length, limited to the nearest centimeter and half or quarter inch.

Clarification 3: When measuring the temperature, limited to the nearest degree.

Clarification 4: When measuring the volume of liquid, limited to nearest milliliter and half or quarter cup.

Clarification 2: Problem types are not expected to include measurement conversions.

Clarification 3: Instruction includes the comparison of attributes measured in the same units.

Clarification 4: Units are limited to yards, feet, inches; meters, centimeters; pounds, ounces; kilograms, grams; degrees Fahrenheit, degrees Celsius; gallons, quarts, pints, cups; and liters, milliliters.

Clarification 2: Number lines, scaled by 50s, 100s or 1,000s, must be provided and can be a representation of any range of numbers.

Clarification 3: Within this benchmark, the expectation is to use symbols (<, > or =).

Example: The number 745 is rounded to 700 when rounded to the nearest 100.

Clarification 2: Within the benchmark, it is the expectation that one problem can be represented in multiple ways and understanding how the different representations are related to each other.

Clarification 3: Factors and divisors are limited to up to 12.

Example: The product of 6 and 300 is 1,800.

Example: The quotient of 27 and 9 is 3.

Clarification 2: Fractions within problems must reference the same whole.

Clarification 3: Within this benchmark, the expectation is not to simplify or use lowest terms.

Clarification 4: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

Example: Clay is running a 10K race. So far, he has run kilometers. How many kilometers does he have remaining?

Clarification 2: Problems include the unknown on either side of the equal sign.

Clarification 3: Multiplication is limited to factors within 12 and related division facts.

Clarification 2: The numbers 0 and 1 are neither prime nor composite.

Clarification 2: Instruction includes recognizing how the numerator and denominator are affected when equivalent fractions are generated.

Clarification 2: Instruction includes using benchmark quantities, such as 0, , , and 1, to compare fractions.

Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

Clarification 4: Within this benchmark, the expectation is to use symbols (<, > or =).

Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms.

Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms.

Clarification 2: When identifying angles, the expectation includes two-dimensional figures and real-world pictures.

Clarification 1: Instruction includes measuring given angles and drawing angles using protractors.
Clarification 2: Instruction includes estimating angle measures using benchmark angles (30°, 45°, 60°, 90° and 180°).
Clarification 3: Instruction focuses on the understanding that angles can be decomposed into non-overlapping angles whose measures sum to the measure of the original angle.

Clarification 2: Problems involving multiplication are limited to products of up to 3 digits by 2 digits. Problems involving division are limited to up to 4 digits divided by 1 digit.

Clarification 3: Responses include the appropriate units in word form.

Clarification 2: Within this benchmark, rectangles are limited to having whole-number side lengths.

Clarification 3: Problems involving multiplication are limited to products of up to 3 digits by 2 digits. Problems involving division are limited to up to 4 digits divided by 1 digit.

Clarification 4: Responses include the appropriate units in word form.

Clarification 2: Scaled number lines must be provided and can be a representation of any range of numbers.

 Clarification 3: Within this benchmark, the expectation is to use symbols (<, > or =).

Example: The number 2,550 is rounded to 3,000 when rounded to the nearest 1,000.

Clarification 2: Instruction includes the use of models or equations based on place value and the distributive property.

Clarification 2: Estimating quotients builds the foundation for division using a standard algorithm.

Clarification 3: When estimating the division of whole numbers, dividends are limited to up to four digits and divisors are limited to up to two digits.

Example: The quotient of 1,380 and 27 can be estimated as 50 because 27 is close to 30 and 1,380 is close to 1,500. 1,500 divided by 30 is the same as 150 tens divided by 3 tens which is 5 tens, or 50.

• Cultivate a community of growth mindset learners. 
• Foster perseverance in students by choosing tasks that are challenging. 
• Develop students’ ability to analyze and problem solve. 
• Recognize students’ effort when solving challenging problems.

• Help students make connections between concepts and representations.
• Provide opportunities for students to use manipulatives when investigating concepts.
• Guide students from concrete to pictorial to abstract representations as understanding progresses.
• Show students that various representations can have different purposes and can be useful in different situations. 

• Provide students with the flexibility to solve problems by selecting a procedure that allows them to solve efficiently and accurately.
• Offer multiple opportunities for students to practice efficient and generalizable methods.
• Provide opportunities for students to reflect on the method they used and determine if a more efficient method could have been used. 

• Establish a culture in which students ask questions of the teacher and their peers, and error is an opportunity for learning.
• Create opportunities for students to discuss their thinking with peers.
• Select, sequence and present student work to advance and deepen understanding of correct and increasingly efficient methods.
• Develop students’ ability to justify methods and compare their responses to the responses of their peers. 

• Help students recognize the patterns in the world around them and connect these patterns to mathematical concepts.
• Support students to develop generalizations based on the similarities found among problems.
• Provide opportunities for students to create plans and procedures to solve problems.
• Develop students’ ability to construct relationships between their current understanding and more sophisticated ways of thinking.

• Have students estimate or predict solutions prior to solving.
• Prompt students to continually ask, “Does this solution make sense? How do you know?”
• Reinforce that students check their work as they progress within and after a task.
• Strengthen students’ ability to verify solutions through justifications. 

• Provide opportunities for students to create models, both concrete and abstract, and perform investigations.
• Challenge students to question the accuracy of their models and methods.
• Support students as they validate conclusions by comparing them to the given situation.
• Indicate how various concepts can be applied to other disciplines.

2-3 Students include relevant textual evidence in their written and oral communication. Students should name the text when they refer to it. In 3rd grade, students should use a combination of direct and indirect citations.

4-5 Students continue with previous skills and reference comments made by speakers and peers. Students cite texts that they’ve directly quoted, paraphrased, or used for information. When writing, students will use the form of citation dictated by the instructor or the style guide referenced by the instructor. 

6-8 Students continue with previous skills and use a style guide to create a proper citation.

9-12 Students continue with previous skills and should be aware of existing style guides and the ways in which they differ.

In grades 1-2, students build upon these skills by justifying what they are thinking. For example: “I think ________ because _______.” The collaborative conversations are becoming academic conversations.

In grades 3-12, students engage in academic conversations discussing claims and justifying their reasoning, refining and applying skills. Students build on ideas, propel the conversation, and support claims and counterclaims with evidence.