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Partition circles and rectangles into halves, fourths, quarters, and use the phrases " Half of, fourth of, and quarter of"

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Partition shapes into Rows and columns :

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Partition shapes into Rows and columns :

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Splitting a rectangle into same size rows and columns with the same size squares

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Creating equal sized shares. Splitting rectangles and circles into twos, threes, and fours

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Develop understanding of fractions as numbers: 

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Develop understanding of fractions as numbers: 

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The numerator is one part of the denominator which is the whole.
Example: if the fraction is 5/6 there are 5 parts out of 6 which represent the whole

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Understand a fraction as a number on the number line:

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Understand a fraction as a number on the number line:

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Represent a fraction ( 2/3) on a number line by defining an interval from 0 to 1. Represent 2/3 on a number line by marking off lengths of thirds from 0 to 1.

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Explain equivalence of fractions in specific cases:

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Explain equivalence of fractions in specific cases:

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Understanding the fractions are equivalent or equal if they are the same size. Students will express whole numbers in fraction form for example 3/1 = 3. When students compare two fractions they need to understand that the comparison is only valid when the to fractions refer to the same whole.

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Extend understanding of fraction equivalence and ordering:

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Extend understanding of fraction equivalence and ordering:

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When you multiply the top and bottom number by the same number it is going to make an equivalent fraction.

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

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

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Comparing two fractions with the same numerator or denominator: 

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Comparing two fractions with the same numerator or denominator: 

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Use equivalent fractions as a strategy to add and subtract 

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Use equivalent fractions as a strategy to add and subtract 

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Add and subtract fractions with unlike numerators and denominators, by replacing fractions with equivalent fractions.

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Interpret a fraction as division of the numerator by the denominator.

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Use understandings to multiply a fraction or whole number by a fraction:

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Use understandings to multiply a fraction or whole number by a fraction:

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interpret the product (a/b) x q as a partition of q into b equal parts.
(a x q)  / b.

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Use understandings of division to divide unite fractions by whole number and whole numbers by unit fractions. 

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Use understandings of division to divide unite fractions by whole number and whole numbers by unit fractions. 

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Interpret division of a unit fraction by a non-zero whole number. Interpret division of a whole number by a unit fraction. Use these methods to solve real world problems.

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Apply and extend previous understandings of multiplication and division to divide by fractions: 

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Apply and extend previous understandings of multiplication and division to divide by fractions: 

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Interpret and compute quotients of fractions and solve real world problems involving division of fractions by fractions. Apply use of visual models.

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Understand decimal notation for fractions, and compare decimal fractions. 

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Understand decimal notation for fractions, and compare decimal fractions. 

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

Use decimal notation for fractions with denominators 10 or 100 and be able to compare two fractions that refer to the same whole.

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Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number.

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Multiplication of fractions and mixed numbers:

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Multiplication of fractions and mixed numbers:

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Solving real world problems with by multiply fractions and mixed numbers.

A recipe calls for 3/4 of a cup of flour. If you double the recipe, how much flour do you need?

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Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.  

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Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.  

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Represent addition and subtraction on a horizontal or vertical number line diagram.

Understand that integers can be divided, provided that the divisor isn't zero.

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In eigth grade students should be able to use previous grades and knowledge about fractions to apply to new information and real world problems.