Math

4J has adopted LearnZillion as our math curriculum and this will be most students’ second year with the curriculum. It is entirely on-line and each student has access to the lessons and practice problems. This curriculum is aligned to the Common Core State Standards and will push the students to dig deeper in their mathematical understanding. In order to help them communicate their ideas, we will be keeping math journals! This is a great resource and will help them become more independent mathematician!

Unit 4: Decomposing and Composing Fractions for Addition and Subtraction

In this unit, students begin to integrate their understanding of fractions with their understanding of operations. The unit begins with the idea of “reasoning up and down”, which reinforces the meaning of fractions and the components of fractions. Students reason from non-unit fractions “down” to unit fractions, and then reason “up” to wholes and then to other fractions with the same denominator. This process prepares students for future reasoning with ratios, and insures understanding of the numerator and denominator.

Students then use their grasp of addition and subtraction to discover the different ways of composing and decomposing fractions, which they have previously only partitioned into unit fractions. The emphasis on lengths helps students connect their understanding of types of addition and subtraction problems with whole numbers to the new type of number: fractions. In the final three lessons, operations and decomposition are further extended to include mixed numbers.

By rewriting, decomposing, adding, and subtracting fractions, students deepen their understanding of equivalence and operations. Students see equivalent lengths throughout the unit, reinforcing an idea they learned in previous grades about the invariance of a length. For instance, a length of 2/8 is determined by a point that is a distance of 2/8 from zero, but that length occurs in infinitely many places along the number line. 

Standards: 

4.NF.B.3: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 

3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b .

  • Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
  • 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. 
  • Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Strategies:

 

 

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