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Fourth grade math features addition and subtraction of like fractions, adding and subtracting mixed numbers, improper fractions and mixed numbers, comparing and ordering fractions and equivalent fractions.

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Fourth grade math features addition and subtraction of like fractions, adding and subtracting mixed numbers, improper fractions and mixed numbers, comparing and ordering fractions and equivalent fractions.

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Fifth grade math features using equivalent fractions as a strategy to add and subtract the fractions. It also features applying and extending previous understandings of multiplication and division to multiply and divide fractions.

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Fifth grade math features using equivalent fractions as a strategy to add and subtract the fractions. It also features applying and extending previous understandings of multiplication and division to multiply and divide fractions.

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4.NF.1 Explain why a fraction is equivalent to a fraction 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.

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4.NF.1 Explain why a fraction is equivalent to a fraction 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.

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Third grade math features mixed and equivalent fractions, fraction conversion, adding and subtracting fractions, and comparing like fractions.

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Third grade math features mixed and equivalent fractions, fraction conversion, adding and subtracting fractions, and comparing like fractions.

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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.

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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.

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5.NF.1 Add or Subtract fractions with unlike denominators- to create a sum that has like denominations 

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5.NF.1 Add or Subtract fractions with unlike denominators- to create a sum that has like denominations 

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3.NF.1 Develop understanding of fractions as numbers. 

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3.NF.1 Develop understanding of fractions as numbers. 

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Students will have an understanding that a fraction represents a part of a whole. A fraction is composed of pieces of a unit fraction, which has a numerator of 1.

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5.NF.2 Be able to solve word problems by adding and subtracting fractions. Use drawings and estimation.

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5.NF.2 Be able to solve word problems by adding and subtracting fractions. Use drawings and estimation.

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5.NF.3 Solve word problems using division of whole numbers to produce a fraction. 

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5.NF.3 Solve word problems using division of whole numbers to produce a fraction. 

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3.NF.2 Students determine fractions through labeling a number line.

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3.NF.2 Students determine fractions through labeling a number line.

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5.NF.4a Interpret the product as parts of a partition. 4b Find the area of a rectangle with fractions as the lengths.

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5.NF.4a Interpret the product as parts of a partition. 4b Find the area of a rectangle with fractions as the lengths.

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5.NF.5a Without preforming multiplication, compare two factors. 5b Explain why multiplying a given number by a fraction greater than 1 results in a product greater and smaller than the given number.

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5.NF.5a Without preforming multiplication, compare two factors. 5b Explain why multiplying a given number by a fraction greater than 1 results in a product greater and smaller than the given number.

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5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.

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5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.

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5.NF.7a Interpret division of a unit fraction 

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5.NF.7a Interpret division of a unit fraction 

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3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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3.NF.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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3.NF.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

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3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

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3.NF.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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3.NF.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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

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

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4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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4.NF.3b 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.

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4.NF.3b 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.

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4.NF.3c 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.

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4.NF.3c 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.

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4.NF.3d 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.

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4.NF.3d 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.

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

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

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4.NF.4a Students 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).

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4.NF.4a Students 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).

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4.NF.4b 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.)

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4.NF.4b 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.)

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4.NF.4c 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?

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4.NF.4c 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?

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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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

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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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

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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 0.62 meters; locate 0.62 on a number line diagram.

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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 0.62 meters; locate 0.62 on a number line diagram.

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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. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

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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. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

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Sixth grade math features understanding ratio concepts and use ratio reasoning to solve problems.

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Sixth grade math features understanding ratio concepts and use ratio reasoning to solve problems.

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6.RP.1 Understand the concept of a ratio and use ratio language to describe  a ratio relationship between two quantities.

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6.RP.1 Understand the concept of a ratio and use ratio language to describe  a ratio relationship between two quantities.

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6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b not equalling 0, and use rate language in the context of a ratio relationship.

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6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b not equalling 0, and use rate language in the context of a ratio relationship.

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6.RP.3a Make tables of equivalent rations relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values of the coordinate plane.

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6.RP.3a Make tables of equivalent rations relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values of the coordinate plane.

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6.RP.3a rates and ratios word problems 1.7

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6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.

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6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.

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6.RP.3c Find a percent of a quantity as a rate per 100, solve problems involving finding the whole, given a part and the percent.

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6.RP.3c Find a percent of a quantity as a rate per 100, solve problems involving finding the whole, given a part and the percent.

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6.RP.3d Use ratio reasoning to convert measurement units, manipulate and transform units appropriately when multiplying or dividing quantities.

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6.RP.3d Use ratio reasoning to convert measurement units, manipulate and transform units appropriately when multiplying or dividing quantities.