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Develop understanding of fractions as numbers.
3.NF.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)
Activities:
Connect unit fractions to fair shares a cookie shared by 2, 3 or 4 using fraction circles; a pizza shared by 2, 4 or 8; candy bars (Hershey bar fractions); a pan of brownies shared by 2, 4, 8; 3, 6, 12
Divide a whole into successively smaller pieces (the Pizza Pirate story: each day the Pizza Pirate eats 1/2 of whats left. Rip paper to show this. Make a table to show how much is left each day.)
3.NF.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)
Activities:
Make strip models from paper by folding and unfolding, then half the group cut theirs. Line up by size to see the pattern in denominators; line up to make a number line. Combine two sets to make a number line to 2.
3.NF.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. 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.
c. 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.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their sizes. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, < and justify the conclusions, e.g., by using a visual fraction model.
Activities:
Use fraction circles to generate equivalent fractions.
Do the same with strip models or fraction bars.
Use fraction bars along the number line to rename 1/2 as fourths, 3/4 as eighths, 1 as thirds, etc. Students can make as many equivalent fractions as they can in this way. What are the names of all the halves?
Use fraction circles to reason about fractions with the same denominator: Which is larger, 3/5 or 4/5? Which is smaller, 3/8 or 4/8? Why?
But ask, which is more, 3/4 of a small pizza or 2/4 of a large pizza?
Use fraction circles to reason about fractions with the same numerator: Which is larger, 3/5 or 3/4? Which is smaller, 3/8 or 3/10? Why?
Reason with shapes and their attributes.
3.G.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.
Activities:
Introduce fraction squares
Geometric shapes that can and cant be easily divided into equal parts (black line master)
4th Grade Common Core
Extend understanding of fraction equivalence and ordering.
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. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Activities:
CRA for equivalent fractions: Develop the procedure of scaling up through the use of fraction circles. Show that 1/2, 2/4 and 4/8 are the same size, then look for a pattern between the numerators and denominators. Make a table of numerators and denominators, if that helps.
Extend the concept of scaling up to scaling down.
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. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Activities:
Reason about the size of fraction circle pieces: Use 1/2 and 1 as anchor numbers for comparing the size of fractions. Develop facility with comparisons to 1/2 and 1 through the use of fraction circles. Use the Comparing and Ordering Fractions worksheet.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
4.NF.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
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.
Activities:
Use the section of the student packet on adding fractions with the same denominators.
4.NF.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
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?
Activities:
Use the section of the student packet on multiplying a fraction by a whole number.
4th Grade Common Core (cont)
Understand decimal notation for fractions, and compare decimal fractions.
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. (Addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, &100.)
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. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
4.NF.7
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when 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. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Activities for 4.NF.5-7:
Use coins to represent 1/100, 1/10, 1. Build decimal numbers using dimes and pennies (e.g. .54 = 5 dimes and 4 pennies, or .5 + .04).
Use the hundredths graphic to equate tenths and hundredths. For each pair of equivalent fractions, recognize how one is scaled up to the other.
Scale down from hundredths to tenths when possible, such as 80/100. Explain why numbers such as 85/100 do not have equivalent tenths.
Write each in decimal notation.
Use the Decimal Assessment worksheet.
Problem-solving
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.MD.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Activities:
Represent and interpret data.
4.MD.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
Activities:
Geometric measurement: understand concepts of angle and measure angles.
4.MD.5
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
Activities:
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