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Common Core Learning StandardsGRADE 4 Mathematics

NUMBER & OPERATIONS – FRACTIONS

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Extend understanding of fraction equivalence and ordering.

Fractions Calculate equivalent fractions. numerator denominator equivalent fraction equivalent

forms of 1

Draw a fraction model to identify equivalent fractions.

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.

Explain why multiplying a fraction by an equivalent form of 1 (2/2, 3/3, etc) results in an equivalent fraction.

SAMPLE TASKSIa. Jeremiah and Susan each had the same size pizza. Jeremiah’s pizza was cut into 8 slices, and he ate 3 of those slices. Susan’s pizza was cut into 4 slices, and she ate 1 of those slices. Who ate more pizza? Show all your mathematical thinking.

Ib. Explain how you figured out your answer by making a comparison of the fractions. ____________________________________________

___________________________________________________________________________________________________________________

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.


Extend understanding of fraction equivalence and ordering.

Comparing fractions with

unlike denominators

Compare and order two fractions with unlike numerators and denominators by creating common denominators or common numerators.

numerator denominator common

denominator common

numerator benchmark

fractions visual fraction

model greater than less than equal to

Compare and order two fractions with unlike numerators and denominators by comparing them to benchmark 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.

Explain that comparisons between two fractions are only valid when referring to the same whole.Record comparisons between fractions with less than, greater than, or equal to symbols.Justify comparison between two fractions using a visual fraction model.

SAMPLE TASKSSee Below

Ia. Damario needs 2/8 cup of milk and 1/3 cup of water to make pancakes. Does he need more milk or more water to make the pancakes? Show all your mathematical thinking.

Ib. Explain how you figured out your answer by making a comparison of the fractions. ____________________________________________


___________________________________________________________________________________________________________________

II. Megan used ½ cup of flour, 2/8 cup of baking soda, and ¾ cup of sugar for a recipe. Use the number line below to help you to identify the equivalent fractions. Did Megan use more baking soda or more sugar? Show your mathematical thinking.

Answer: __________________________________________


Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Adding and subtracting

fractions

Explain adding fractions as joining parts of the same whole.

numerator denominator part whole fractions

Explain subtracting fractions as separating parts of the same whole.


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

SAMPLE TASKSI. Shade in the fractions using the models below. Find the sum. 5/9 + 2/9 = _________

= + =



Decomposing fractions

Rewrite a fraction into a sum of smaller fractions with the same denominator.

sum fraction decomposition visual fraction

Write each decomposition as an equation.


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.

Explain why rewriting a fraction is equivalent to the original fraction by using a visual fraction model.

SAMPLE TASKSI. Show the fraction 3/8 as an equation. a. Show the fraction as unit fractions 3/8 = ____ + ____ + ____ b. Explain why the number sentence above is true.

c. Use the model below to show the fraction 3/8 as unit fractions.



Addition and subtraction of

mixed numbers

Add mixed numbers with like denominators using properties of operations, equivalent fractions, and the relationship between addition and subtraction.

mixed number improper

fraction equivalent numerator

Subtract mixed numbers with like denominators using properties of operations, equivalent fractions,


and the relationship between addition and subtraction.

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.

Convert mixed numbers to improper fractions to add and subtract fractions with like denominators.

SAMPLE TASKS(See Below)

I. Nancy has a red ribbon that is 318 feet long. She also has a purple ribbon that is 1

58 feet long. How many feet longer is the red ribbon

than the purple ribbon? Show all your mathematical thinking.

II. Kelley drank 126 cups of water in the morning and 2

16 cups of water in the afternoon. How much water did Kelley drink in all? Show all

your mathematical thinking.




Addition and subtraction of fractions with

word problems

Identify the operation needed to solve a word problem.

numerator denominator equation whole total difference sum visual fraction

model equation

Solve word problems that involve addition and subtraction of fractions with like denominators referring to the same whole.

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.

Draw visual fraction models or create equations to representing word problems.

SAMPLE TASKSI. Debbie spent 2/6 hour reading and 3/6 hour studying for her math quiz. How long did Debbie spend reading and studying for the quiz? Show all your mathematical thinking.

II. There was ¾ of a pad of paper on the counter. Gretchen used ¼ of the pad to write thank you letters. What fraction of pad of paper is left? Show all you your mathematical thinking.




Rewriting fractions

Identify the relationship between repeated addition and multiplication.

multiple numerator denominator unit fraction

Rewrite a fraction as a unit fraction (numerator = 1) with the same denominator multiplied by the numerator written as a whole number. (See standard example).

4.NF.4a. 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).

Generate multiples of the fraction 1/b.

SAMPLE TASKSIa. Saul put ½ bags of pretzels in his lunch box each day for 4 days. How many bags of pretzels did Saul put in his lunch box in all? Show your mathematical thinking.

Ib. Show a different way to solve the problem.


II. Howie has 9 baskets. Each basket is 1/3 full of tomatoes. IIa. Make a model to show this problem.

IIb. How many full baskets of tomatoes does Howie have? Use multiplication. Show all your mathematical thinking.


Common Core Learning Standards

Concepts Embedded Skills Vocabulary


Multiply fractions and whole numbers

Multiply a fraction by a whole number by decomposing the fraction as the numerator multiplied by the unit fraction of its denominator.

Fraction Whole number Multiple Multiply Product Unit fraction Numerator Denominator

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.)

SAMPLE TASKSSee Below

I. Fill in the blank with the appropriate whole number.

3 x = ____ x


II. How many 28 are needed to make 68? Show your mathematical thinking.




Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers

Multiplication of fractions and word problems

Create a numeric expression from a word problem involving the multiplication of a whole number and a fraction.

Multiply Whole

number Fraction Numerator Denominator

Solve word problems involving the multiplication of whole numbers and fractions.

Identify between what two whole numbers the solution lies.

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?

SAMPLE TASKS (See Below)

Ia. Joe is baking cookies. The recipe calls for ¼ cup of flour, but Joe is making 5 batches. How Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

many cups of flour will Joe need? Create an equation to solve the problem.

Ib. Between which two whole numbers does the solution lie? ______ and ______




Understand decimal notation for fractions, and compare decimal fractions.

Adding fractions Convert fractions with a denominator of 10 to an equivalent fraction with a denominator of 100.

Numerator Denominator Equivalent fractions add

Add two fractions with denominators of 10 and 100.

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

SAMPLE TASKSI. Fill in the blank to make the open number sentence true.

3/10 = ___ /100


II. 6/10 + 4/100 = _______

IIa. Explain how you found your answer.

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________





Conversion of fractions to

decimals

Convert fractions with denominators of 10 and 100 to decimals.

Decimal Tenths Hundredths Number line Fractions Denominator Numerator

Locate decimals on a number line.

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.

Describe lengths in decimal form.

SAMPLE TASKS

I. Rod’s puppy ate 810of a can of dog food. Write the equivalent decimal amount of the dog food

that Rod’s puppy ate. ________________________________

II. Place the following decimals on the number line below. 0.3 , 0.6 , 0.8


III. The point on the number line below shows the height of a ladder.

Meters

Express the height of the ladder in decimal form. ___________________ meters

Common Core Learning Concepts Embedded Skills VocabularyCopyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

0 1 2

Standards


Comparing and ordering decimals

Compare and order decimals to hundredths. Greater than Less than Equal to Tenths Hundredths Decimals Visual fraction model

Draw a visual model to reason about the size of decimals.

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.

Explain that comparisons between two decimals are only valid when referring to the same whole.

Compare decimals using greater than, less than, and equal to symbols.

SAMPLE TASKSI. Order the following decimals from greatest to least.

.25 .8 .01 .37 .10

_________ _________ _________ _________ _________


II. Using the grid below, explain why .6 is greater than .06.

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

III. Sue ate ¼ of her small, personal-sized pizza. Mark said he would be eating the same amount if Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

he ate ¼ of the large, party pizza. Use the model below to determine if Mark was correct.

Sue’s Pizza Mark’s Pizza

Explain your thinking. ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


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