Math unit 6 - The next unit of study in our math continuum once again will focus on fractions, unit fraction and greater number understanding. This unit will pick up where we left off, just a few months ago, when our students were studying fractional parts, equivalent fractions and ordering fractions. This unit will get deeper into some of the operations with fractions (adding & subtracting fractions along with working more with mixed numbers and improper fractions.). Along with developing these specific stills and standards, the students will also be asked to model and use their own logic and explanation to express the structure of some numbers and fractions.
Here is a list of specific 4th grade standards covered in this unit: MP 1:Make sense of problems and persevere in solving them. MP 2: Reason abstractly and quantitatively. MP 3: Construct viable arguments and critique the reasoning of others. MP 4: Model with mathematics. MP 5: Use appropriate tools strategically. MP 6: Attend to precision. MP 7: Look for and make use of structure. MP 8: Look for and express regularity in repeated reasoning. 4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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. 4.NF.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 4.NF.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. 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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. 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. d. 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. 4.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand 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 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3×(2/5) as 6×(1/5), recognizing this product as 6/5. (In general, n×(a/b)=(n×a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?