Math:

Math Quarter 2

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (nxa)/(nxb) 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.

1. I can understand the value of a fraction. -I will explain the value of the numerator and the value of the denominator.

I will explain the relationship between the numerator and denominator. (part to whole)

2. I can understand how a fraction model represents a fraction.

I will explain how the fraction model represents a fraction.

I will draw a fraction model to represent a fraction.

3. I can understand how two fractions are equivalent. -I will explain what equivalent means.

I will explain the relationship between two equivalent fractions, and why they are equivalent.

4. I can understand how two different looking fraction models are equal to the same value.

I will examine the relationship between two different looking fraction models.

I will use various methods to model equivalent fractions (modeling, drawing, computation)

4.NF.2 Compare two visual models of fractions with different denominators and different numerators

1. I can recognize that two fractions with the same denominator and different numerators have a different value.

I will use models and draw pictures to show that fractions with the same denominator but different numerators represent different values.

2. I can use the symbols >, <, or = to compare the value of fractions with same denominator and different numerators.

I will determine which numerator is larger.

I will indicate the relationship between the two fractions by writing an expression using the >, <, = symbols.

3. I can recognize that two fractions with different denominators and same numerators represent different values.

I will use models and draw pictures to show that fractions with different denominators but same numerators represent different values.

4. I can use the symbols >,<, or = to compare the value of fractions with different denominators and the same numerator.

I will compare the given fraction to a benchmark fraction or find the common denominator.

I will indicate the relationship between the two fractions by writing an expression using the >, <, = symbols.

5. I can determine whether a fraction is greater than, less than, or equal to a benchmark fraction. (1/4, 1/2, 3/4, 1/10)

I will determine whether a given fraction is greater than, less than, or equal to a benchmark fraction by using models and pictures

6. I can recognize that I can only compare 2 fractions when both fractions refer to the same whole. (using pattern blocks-hexagon = 1, so trapezoid = .)

I will use manipulatives to illustrate the relationship between parts of a whole.

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

1. (a) I can join fractions with a numerator of 1 and the same denominator by adding them.

I will add fractions with common denominators by adding the numerator. The denominator will remain the same.

I will explain why the denominator must remain the same when adding fractions with common denominators.

2. (a) I can separate fractions with the same denominator by subtracting them.

I will subtract fractions with common denominators by subtracting the numerator. The denominator will remain the same.

I will explain why the denominator must remain the same when subtracting fractions with common denominators.

3. (b) I can decompose fractions using fraction models.

I will use manipulatives to demonstrate how fractions with a numerator greater than one can be broken apart into smaller parts. (this includes mixed numbers, improper fractions, and standard fractions)

4. (b) I can write a decomposed fraction (broken apart) using an equation.

I will draw a fraction model to illustrate how I decomposed the fraction.

I will write an equation to explain what my illustration represents.

5. (c) I can add and subtract mixed numbers with like denominators.

I will identify mixed numbers.

I will use a variety of strategies to add and subtract mixed numbers.

(For example: (1) converting a mixed number into an improper fraction, (2) adding whole numbers first then fractions, then adding those two together)

I will use models and drawing to add and subtract mixed numbers with like denominators.

6. (d) I can determine which operation (addition or subtraction)to use when solving word problems involving fractions with like denominators.

I will identify key words.

I will use the correct operation to solve the problem.

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number

1. (a) I can multiply a fraction with a numerator of 1 by a whole number.

I will use repeated addition of fractions to represent the multiplication of a whole number by a fraction.

I will understand the connection between repeated addition and multiplication.

2. (b) I can multiply a fraction with a numerator greater than one by a whole number.

I will use repeated addition and pictures to model my understanding of multiplying a fraction.

3. (c) I can solve word problems that involve multiplying a fraction by a whole number.

I will use a variety of strategies such as diagrams, visual models and equations to solve word problems.

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100

1. I can restate fractions that have a denominator of 10 or 100 as equivalent (Example: 3/10=30/100)

I will demonstrate the relationship between fractions with a denominator of 10 and 100 using models (grids and 100th circles).

2. I can explain the relationship between tenths and hundredths.

I will use a visual model to demonstrate my understanding of the equivalent relationship.

3. I can add two fractions that have a denominator of 10 or 100

(Example: 3/10+4/100=34/100)

I will change fractions with a ten in the denominator into equivalent fractions that have a 100 in the denominator.

I will add two fractions once the denominators are the same.

4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as .62 meters; locate 0.62 on a number line diagram

1. I can convert decimals into fractions, with denominators of 10 or 100

I will use a visual model (number line, place value chart, grid, 100tHcircle) to represent both the fraction and its equivalent decimal.

2. I can convert fractions into decimals, with denominators of 10 or 100

I will use a visual model (number line, place value chart, grid, 100th circle) to represent both the fraction and its equivalent decimal.

I will find and show the relationship between two equivalent fractions with denominators of 10 or 100.

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole

1. I can compare two decimals up to the hundredths place.

I will indicate the relationship between the two decimals by writing an expression using the >, <, = symbols.

2. I can recognize comparisons are only valid when two decimals refer to the same whole.

I will use visual models (area models, decimal grids, decimal circles, number lines, and meter sticks) to compare decimals.