Handout 4.0a [pg. 1 of 2]:

Foundational Standards Review

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Directions:

Below are the foundational standards for your grade level. Read through them and:

• Annotate the text by picking 10 words or phrases that are most relevant to you
• Then, jot down some of your thinking as to why those words and phrases are important

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Numbers and Operations—Fractions: (NY-4.NF)

• Develop understanding of fraction equivalence and operations with fractions; Recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and develop methods for generating and recognizing equivalent fractions; and
• Extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.
• Use 0-2 number lines to represent relative fraction magnitude for fractions less than 1, equal to one, and greater than 1 as well as mixed numbers.

Opportunities for students to develop connections between concepts, strategies, language,

reasoning, and problem solving:

• Illustrating (using equations, arrays, area models or other representations) and explaining strategies based on place value for calculating products, quotients, and remainders of multi-digit whole numbers, helps students combine prior understanding of multiplication with deepening understanding of the base-ten system. This work will continue in grade 5 and culminate in fluency with the standard algorithms in grade 6. Exploring and extending fraction equivalence to the general case using visual fraction models and through reasoning about number and size of parts allows students to extend arithmetic from whole numbers to fractions and decimals.

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Math | Module 4.0 (Gr 4)

Handout 4.0a [pg. 2 of 2]:

Foundational Standards Review

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• Understanding that all fractions can be thought of as the sum of unit fractions with the same denominator represents an important step in the multigrade progression for addition and subtraction of fractions. Students extend their prior understanding of addition and subtraction to add and subtract fractions with denominators by thinking of adding or subtracting so many unit fractions.
• Extending previous understandings of multiplication to multiply a whole number by a fractions is an important step in the multigrade progression for multiplication and division of fractions. Students extend their developing understanding of multiplication to multiply a fraction by a whole number.

Math | Module 4.0 (Gr 4)

Handout 4.0b:

Tips: Getting the Most Out of Your Module

• Create opportunities for collaboration with colleagues. Learning is always done better together.
• Do the math. Anytime you are prompted to do math as part of the session, take the time and think through how you would approach the problem AND how your students might solve the problem. There are many strategies that may come up. Doing the math in this way provides you deep insight into student thinking and math content development.
• Do the Bridge to Practice work. Taking your learning back to the classroom is an essential part of your development.
• Implement new resources or approaches many times. Give you and your students time and grace as you shift to a more meaningful math practice.

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Math | Module 4.0 (Gr 4)

Handout 4.0c [pg. 1 of 2]:

Terminology

Generalization

• The underlying mathematical structures that are always true. (For example, the commutative property of addition a + b = b + a).

Instructional Core

• The instructional core includes three interdependent components: teachers’ knowledge and skill, students’ engagement in their own learning, and academically challenging content.

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Summative Assessment

• The evaluation of student learning, skill acquisition, and academic achievement at the conclusion of a defined instructional period—typically at the end of a project, unit, course, semester, program, or school year.

Formative Assessment

• Practices that provide teachers and students with information about learning as it develops—not just at the end of a project, unit, or year. The information is formative because it enables adjustments that deepen learning; teachers use formative assessment to make adjustments to instruction and students use the feedback from formative assessments to make revisions to their work and their approaches to it.

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Math | Module 4.0 (Gr 4)

Handout 4.0c [pg. 2 of 2]:

Terminology

A note on the term Improper Fraction

• In the math world this term is now obsolete. The recommendation is to use the language “fractions greater than 1 whole.” The reasons are twofold. One, “improper” suggests to students that there is something wrong with the fraction when in fact the notation is completely reasonable and accurate. Two, the language “fractions greater than 1 whole” has much greater mathematical meaning. The language describes what the fraction represents. Most of us were introduced to “improper fractions” when we were in school and learning fractions. This language is also included in many curricular programs. Make a concerted and intentional effort to use the language that makes sense.

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Partitive Division

• When dividing a number into a known number of groups. For example, 8 children sharing 4 brownies, is a partitive division context because 4 is being divided into 8 groups.

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Quotative Division

• When dividing a number into a known measure of each group. For example, a group of children are sharing 4 brownies. Each child gets ½ of a brownie. How many whole brownies did they start with?

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Math | Module 4.0 (Gr 4)