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Pitfalls to avoid when teaching 4.NF.B.3.c

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4.NF.B.3.c is about students applying strategies for adding and subtracting whole numbers to add and subtract mixed numbers. Knowing that a mixed number is the sum of a whole number and a fraction helps students as they compose and decompose mixed numbers to add and subtract.

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For this standard, students will only add and subtract mixed numbers with a common denominator.

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##### 3 ones 1 sixth + 2 ones 2 sixths = 5 ones 3 sixths

It's important for students to understand that a mixed number is the sum of whole number and a fraction and can be decomposed just like a whole number in order to make the numbers easier to work with. To do this, students will use unit form to recognize they need to add or subtract like units (e.g., ones to ones and sixths to sixths).

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like denominators

This indicates that students will complete problems adding and subtracting mixed numbers that have the same denominator.

Students should be representing mixed numbers with equivalent fractions based on their understanding that the number 1 can be represented by a fraction with the same numerator and denominator.

### Unpack the standard

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

3.NF.A.1

3.NF.A.2

4.NF.A.1

4.NF.A.1Explain why a fraction a/b is equivalent to a fraction (n Γ a)/(n Γ b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

3.NF.A.1Understand a fraction 1/π as the quantity formed by 1 part when a whole is partitioned into π equal parts; understand a fraction π/π as the quantity formed by π parts of size 1/π.

3.NF.A.2Understand a fraction as a number on the number line; represent fractions on a number line diagram.

4.NF.B.3.cAdd and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

### Connections to Prior Learning

Click on the yellow index cards below to learn about how these standards connect to 4.NF.B.3.c.

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##### Avoid this pitfall!

The biggest pitfall comes when students are taught a trick to help them navigate from a mixed number to an improper fraction.

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##### Avoid this pitfall!

The biggest pitfall comes when students are taught a trick to help them navigate from a mixed number to an improper fraction.

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##### Avoid this pitfall!

The biggest pitfall comes when students are taught a trick to help them navigate from a mixed number to an improper fraction.Avoid this pitfall by giving students opportunities to make sense of the number and use their understanding of equivalency to replace numbers when necessary.

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4.NF.B.4aUnderstand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

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4.OA.A.2Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

3.OA.A.1Interpret products of whole numbers, e.g., interpret 5 Γ 7 as the total number of objects in 5 groups of 7 objects each.

3.oa.a.1

4.oA.a.2

3.nf.a.1

4.NF.B.4a

3.NF.A.1Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

### Connections to Prior Learning

Click on the index cards below to learn about how these standards connect to 4.NF.B.4a.