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4th Grade Unit of Study

Getting into Fractions

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|Unit of Study |

|Getting into Fractions |

|Grade: 4 |Topic: Numbers and Operations: Fractions |Length of Unit: 12-17 days |

|Focus of Learning |

|Common Core Standards: |Standards for Mathematical Practice: |

|Extend understanding of fraction equivalence and ordering. |Make sense of problems and persevere in solving them. |

|4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual |Reason abstractly and quantitatively. |

|fraction models, with attention to how the number and size of the parts differ even though the |Construct viable arguments and critique the reasoning of others. |

|two fractions themselves are the same size. Use this principle to recognize and generate |Model with mathematics. |

|equivalent fractions. |Use appropriate tools strategically. |

|4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by |Attend to precision. |

|creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. |Look for and make use of structure. |

|Recognize that comparisons are valid only when the two fractions refer to the same whole. Record |Look for and express regularity in repeated reasoning. |

|the results of comparisons with symbols >, =, or , =, < | |

|Concept of equivalency and congruency |Students will attend to precision |

|Parts of a fractions (denominator and numerator) |Students will use academic language such as: |

| |one-whole, zero, half, greater than, less than, equal to, denominator, numerator,|

| |etc.… |

|Which math concepts will this lesson lead to? |Number lines are accurate |

|Compare two fractions with different numerators and/or denominators | |

|Order fractions using a number line and other graphic representations | |

|Essential Question (s) |

|How are fractions related to whole numbers? |

|How can I use different size pieces to create equivalent fractions? |

|How can equivalent fractions be identified? |

|Why are fractions important? |

|How do we compare fractions? |

|How can benchmark fractions be useful in real life? |

|Formative Assessments |

|Thumbs up / thumbs down for agreement throughout lesson |

|Ticket out the door: How do you know 6/7 is closer to one, than it is closer to 1/2 or 0? |

|Anticipated Student Preconceptions/Misconceptions |

|The bigger the denominator the bigger the piece. |

|It doesn’t matter where you shade the unit fraction on a number line when showing more than one part. |

|Materials/Resources |

|Worksheet of number lines |

|12 premade fraction cards |

|C. Rigor: fluency, deep understanding, application and dual intensity |

|What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of the Math Practices? (Detailed Lesson Plan) |

|Warm Up (Teacher Model) |

|Using a number line, label the 0 on the left side, and the 1 on the right side, divide into 2 parts, and shade 1 part. |

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|Draw another number line the same length; again divide into 2 parts, and shade 1 part. |

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|Ask if the shaded parts are equivalent. |

|Divide each part of the second number line into 2 equal pieces. |

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|Ask students to think about how they would label the pieces and if the shaded parts are still equivalent. |

|Lesson |

|Hand out worksheet of number lines |

|Independently: Students will repeat warm up step on the first two number lines on their handout (a and b), then label the new fractions (fourths) |

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|Whole Class: Ask students to share how they labeled the second number line and have them compare 1/4 to 0, 1/2, and 1. |

|Teacher, “When thinking about fractions it is good to have some benchmark fractions to use for comparison. Today we will think about the benchmark fractions 0, |

|1/2, and 1 whole.” |

|How does 1/4th compare to the benchmark fractions? ( 1/4 > 0, 1/4 < 1/2 and 1/4 < 1, 1/4 is |

|equidistance from 0 and 1/2 but farther from 1) |

|Which benchmark fractions are closer to 2/4, 3/4, 4/4? |

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|In pairs: Have individual students label 0, ½ and 1 on the remaining number lines (c, d, and e). |

|Students will then work in pairs to continue making 6 parts, 8 parts, and 10 parts and label the fractional parts. |

|After 2-3 minutes ask pairs to discuss which fractions are closer to 0, 1/2, and 1. |

|Ask students, “Why would knowing the location of 0, 1/2, and 1 on a number line help when comparing fractions?” |

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|Whole Class: Share-out |

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|Teacher draws a large number line on the board labeling only 0, 1/2, and 1. |

|Students make their own number line like the one on the board on the back of their worksheet. |

|Teacher passes out fraction cards to a selection of students or to groups of students. |

|Students are called upon to tell what their fraction is. |

|Before student places fraction card on the front board’s number line, seated students label their number line where they think it should be placed without cutting |

|the number line into more pieces. |

|Called on students then places the fraction card on the number line, class asked to agree or disagree with hand signals, then discuss how they knew where to place |

|the fraction on the number line. (note: we are looking for students to refer to the benchmark fractions. for example: “I knew 8/9 was almost one whole, so I put it|

|on the number line close to 1.”) |

|Continue with each of the other cards. |

|Closure |

|Ticket out the door: What is 6/7 closer to 0, 1/2, or 1? How do you know? |

|Suggested Homework/Independent Practice |

|Homework sheet |

a)number line

b)number line

c)number line

d)number line

e)number line

|2 |7 |1 |2 |

|3 |9 |10 |99 |

|3 |3 |11 |2 |

|5 |7 |12 |18 |

|9 |89 |4 |6 |

|20 |90 |9 |13 |

Flash Cards for Whole Class Activity

Ticket out the door Name____________________________ Date_______________

Ticket out the door: What is 6/7 closer to 0, 1/2, or 1? How do you know?

Ticket out the door Name____________________________ Date_______________

Ticket out the door: What is 6/7 closer to 0, 1/2, or 1? How do you know?

Ticket out the door Name____________________________ Date_______________

Ticket out the door: What is 6/7 closer to 0, 1/2, or 1? How do you know?

Homework

Name____________________________ Date_______________

1. What is [pic] closer to 0, [pic] , or 1? How do you know?

2. Name three fractions that are closer to 1 whole than they are to [pic].

3. Amie says that [pic] of a Snickers candy bar is larger than [pic]of a Snickers candy bar, but Rachel doesn’t agree. Who do you agree with and why?

Use the space below to draw pictures, use numbers, and write words to justify your thinking.

SCUSD Common Core Mathematics Lesson Planning Guide

|Unit Title: Getting into Fractions |Approx. time: |CCSS-M Standards: 4.NF.1 4.NF.2 |

|Lesson 4: Ordering Unit Fractions |1 day | |

|A. Focus and Coherence |B. Evidence of Math Practices |

|Students will know… |What will students produce when they are making sense, persevering, |

|The size of the whole matters when expressing relationships with |attending to precision and/or modeling, in relation to the focus of |

|fractions |the lesson? |

| | |

|Students will be able to… |Students will make sense of problems and persevere in solving them: |

|Identify, build, read, write, label, compare fractions |“The smaller the denominator the larger the fractional piece.” |

| |“The larger the denominator the smaller the fractional piece.” |

|Student prior knowledge: |“The denominator tells me the number of equal size pieces.” (i.e. ½ |

|Fractional parts are used to make up a whole |means the whole is cut into 2 equal size pieces.) |

|How many pieces it takes to make a whole and each piece is a unit |“It will take more tenths to measure my desk than it will take sixths,|

|fraction |because the tens are smaller than the sixths.” |

|Know what a numerator and denominator are and what they signify |“Ken’s measuring tool was longer than Sam’s measuring tool because 1/3|

| |is greater than 1/4.” |

|Which math concepts will this lesson lead to? |“If I put my 1/3 and 1/4 side by side, it will take more fourths to |

|Comparing and ordering fractions with common denominators |equal one whole length.” |

| | |

| |Students will attend to precision: |

| |denominator |

| |numerator |

| |one-half, one-fourth, one-seventh… |

| |fraction is a part of a whole piece/set |

|Essential Question(s): |

|How do I compare fractions? |

|How are fractions used in real life? |

|Formative Assessments: |

|Have students put the following fractions in order from least to greatest: 1/10, 1/2/, 1/5, 1/25 |

|and add two more unit fractions to this list of their choosing. |

|Then have students explain how they knew which fraction was the least, and which was the greatest. |

|Anticipated Student Preconceptions/Misconceptions: |

|As the denominator increases, students do not understand that the fraction pieces decrease in size. |

|Just because the numerator is larger does not mean that the fraction is in fact larger. |

|Materials/Resources: |

|Mathematics International Grade 4 B44-B45 |

|C. Rigor: fluency, deep understanding, application and dual intensity |

|What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of the Math Practices? (Detailed Lesson Plan) |

|Warm Up |

|Teacher should pose the following question to the class. Students should be given independent think time prior to whole class share-out. (This problem can be done|

|on white boards or paper) |

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|Paul and his brother were eating the same kind (and size) of candy bar. Paul had cut his candy bar into 4 pieces. His brother cut his candy bar into two pieces. |

|If each boy only ate one of their pieces, who ate the most candy bar? |

|Lesson |

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|Hands-on experience: |

|Give students strips of paper and have them cut or fold each into half, fourths and sixths. |

|Use these strips to measure objects in the classroom. |

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|In small groups have students discuss what they discovered through the measuring activity. |

|Allow students 3-6 minutes to work with a partner to explain their understanding and come to an agreement. |

|Have 2-3 students share out giving class the chance to agree or disagree. |

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|Ask Class: |

|Would it take more sixths or tenths to measure the length of your desk/table? |

|Repeat with other unit fractions as needed. |

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|Give students independent think time of 2-3 minutes. |

|Allow students 3-6 minutes to work with a partner to explain their understanding and come to an agreement. |

|Have 2-3 students share out giving class the chance to agree or disagree. |

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|Have students put the unit fractions used into order from least to greatest. |

|Closure: |

|Using page B45 (Mathematics International), have the students explain in words why ½ is larger than 1/3, why 1/7 is less than 1/5. |

|Suggested Homework/Independent Practice: |

|Have students order the following unit fractions from least to greatest and justify their answer with a visual representation: |

|1/17, 1/10, 1/6, 1/12, 1/20, 1/1, 1/2, 1/88… |

Homework

Name________________________________ Date _____________________

Order the following unit fractions from least to greatest and justify their answer with visual representations.

[pic]

SCUSD Common Core Mathematics Lesson Planning Guide

|Unit Title: Getting into Fractions |Approx. time: |CCSS-M Standards: 4NF1 4NF2 |

|Lesson 5: Comparing Fractions with Common Denominators |1 Day | |

|A. Focus and Coherence |B. Evidence of Math Practices |

|Students will know… |What will students produce when they are making sense, persevering, attending to |

|when comparing fractions the whole must be the same, fractions can be represented|precision and/or modeling, in relation to the focus of the lesson? |

|as part of a whole, parts of a set, parts of an area, as a measure, and as a | |

|number on the number line |Students will make sense of problems and persevere in solving them: |

|fractions with like denominators can be compared. |“I know that 3/8 is less than 5/8 because it takes more 1/8 to make 5/8 than it |

| |does to make 3/8.” |

|Students will be able to… |“Since the denominators are the same, I just look at the numerator and that tells|

|identify, build, read, write, label, compare, and represent (as part of a whole,|me which are greater and which are less.” |

|parts of a set, parts of an area, as a measure, and as a number on the number |“The numerator tells me how much of the whole is represented.” |

|line) fractions. | |

|use visual fraction models to justify conclusions. |Students will attend to precision |

| |Students will use academic language such as: |

|Student prior knowledge: |denominator, numerator, fraction, greater than, less than,… |

|Fraction vocabulary (numerator, denominator) | |

|Fractions are parts of wholes | |

|Comparing words and symbols (>, ,

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100 points possible

2 point each

(total 34 problem 1)

4/12, 3/9, 2/6

Possible answers: 5/10, 6/12, 50/100 4/16, 5/20, 25/100 12/16, 15/20 5/15, 6/18, 7/21 4/6, 10/15, 12/18

6/9, 8/12

4/8, 3/6, 2/4

6/8, 9/12

2/8, 3/12

2 point each

(total 10 problem 2)

2 point each

10 points explanation

(total 14 problem 3)

Possible answers:

a) 2/1=20/10 because both fractions are equal to two wholes. If the whole is cut into 1 piece it takes two of those pieces to equal two wholes. If the whole is cut into 10 pieces it takes 20 of those pieces to equal two wholes.

b) 2/2=10/10 because both fractions are equal to one whole. No matter how many equal pieces you cut a whole into, if you take all the pieces you still have one whole.

c) 2/5=4/10 because if you have a whole cut into 5 equal pieces, then you equally divide each of those pieces once more, you will then have 10 equal pieces. The same is true for the two shaded pieces (numerator) of the 2/5 fraction, the 2 pieces become 4 pieces.

d) 2/10=2/10 because the wholes are equally cut into 10 pieces and 2 of those pieces are shaded.

Possible answers: 2/1 = 20/10; 2/2=10/10; 2/5=4/10; 2/10=2/10; 2/20=1/10 …

Possible work:

2 points each

(total 16 problem 4)

6 points work shown

1/2

3/4

2/3

1/4 ................
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