Access Mathematics Grade 4 (#7712050) 

Clarification 2: Depending on the context, the solution of a division problem with a remainder may be the whole number part of the quotient, the whole number part of the quotient with the remainder, the whole number part of the quotient plus 1, or the remainder.

Clarification 3: Multiplication is limited to products of up to 3 digits by 2 digits. Division is limited to up to 4 digits divided by 1 digit.

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: 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: Fractions limited to fractions less than one with denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

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 that data sets can have one mode, no mode or more than one mode.

Clarification 3: Within this benchmark, data sets are limited to an odd number when calculating the median.

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

Clarification 2: Data involving fractions with like denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100. Fractions can be greater than one.

Clarification 3: Data involving decimals are limited to hundredths.

Clarification 2: Instruction includes the understanding that a decimal and fraction that are equivalent represent the same point on the number line and that fractions with denominators of 10 or powers of 10 may be called decimal fractions.

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

Clarification 3: Fractions multiplied by a whole number are limited to less than 1. All denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, 100.

Example: Lacey thinks about finding the product by imagining having 8 pizza boxes each with one-quarter slice of a pizza left. If she put them all together, she would have a total of 2 whole pizzas since which is equivalent to 2.

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: Instruction includes digital measurements and scales that are not linear in appearance.

Clarification 3: When recording measurements, use fractions and decimals where appropriate.

Clarification 2: Within the benchmark, the expectation is not to convert from grams to kilograms, meters to kilometers or milliliters to liters.

Clarification 3: Problems involving fractions are limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

Example: A gallon contains 16 cups. How many cups are in  gallons?

Example: At the grocery store you spend $14.56. If you do not want any pennies in change, how much money could you give the cashier?

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: Within the benchmark, the expectation is to explain the reasoning for the comparison and use symbols (<, > or =). 

Clarification 3: Scaled number lines must be provided and can be a representation of any range of numbers.

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

Clarification 2: Instruction includes the use of models based on place value, properties of operations or the relationship between multiplication and division.

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.

Example: One-tenth more than 2.31 is 2.41.

• 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.