Sample Lessons
The following lessons and activities have been created, keeping in mind the Common Core State Standards and the Common Core Mathematical Practices.
Activity #1
Learning intension: Students will be able to count by halves with a conceptual model in order to write a number multiple ways.
As whole group or small group, provide students with apples that have been cut in half. Discuss with the students that the apples are roughly the same size and that for our purposes we will consider them equal in size. I will ask students to draw a picture and write the number that represents one half, two halves, three halves, etc. Next, I will ask students if they know another way we could write two halves and the four halves. I will then have them with a partner write two ways to express five half apples. Prior to exiting the lesson students should be able independently express an equivalent number for seven half apples. Students may skip count two halves, four halves, and six halves and realize they have three whole apples and then add the remaining half, for a total of three and one half apples. Counting by halves on the number line, students will determine seven half apples is the same as three and a half apples. I would challenge students to identify patterns and to create a number line that represents our discussion of halves. Use attached to record student work.
Activity #2
Learning Outcomes: Students will be able to use the number line as a linear model to demonstrate the fractions of ½ and ¼. Students will identify alternate names for numbers, i.e., two halves equal one whole, two quarters equals 1/2.
Standard: CCSS.Math.Content.3.NF.A.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.
CCSS.Math.Content.3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
Create a K-W-L chart (What do you know about fractions, what do you want to learn and what did you learn)
Students, working with an elbow partner, decide where to place the fraction one half on the number line and share with the class why they placed it there. See Appendix for work sheet.
Question: Where did you place half on the number line? Why did you place it there?
Have students continue placing the halves above the number line, ½, 2/2/, 3/2……. Above the number line, below the line, count by halves: ½. 1 ½, 2, 2 ½ …..
Question: Can you tell me a situation where you count by halves. (Students may associate it with football.)
Questions: Can you name a fraction that is equal to one? Do you notice a pattern, tell me about the numerator and the denominator of a fraction that equals one whole. Two? How many halves equal three? How many halves equal four? Do you notice a pattern? How many halves would equal 6?
Repeat the activity with ¼. Over the course of a week, students should continue to experience placing fractions on a number line, using various unit fractions.
Closing: Students record in their journal one idea they learned about fractions and what they still are wondering about fractions.
Activity# 3: Learning Outcomes:
* Students will identify and match unit fractions and units as they exist in context to real world situations.
* Students will be able to define what a unit fraction as one copy of n equal parts of the whole, and n copies of it will create a whole.
Standard: CCSS.Math.Content.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; or, b copies of 1/b make 1; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Write the word dime on the board. Students should work with a partner or table mates to answer: Describe in a fraction: what is one dime to one dollar? Students should conclude that it is one tenth of a dollar, in that ten dimes make a dollar. Demonstrate how to write 1/10. The 10 in 1/10 is the number of dimes that makes a whole dollar and the 1 refers the one dime. Explain the 1/10 is a unit just like the word dime is a unit. It is a new unit, smaller than the original unit of one dollar. One dime, two dimes, three dimes…or we could count 1/10, 2/10, 3/10…… Give a second example: Write in a fraction what a day is to a week. Students should conclude that there are seven days in a week and one day is 1/7 of a week.
Practice: Students will play a game of concentration in pairs to identify unit fractions to units. The student with the most pairs of unit and unit fractions wins. See Appendix for cards.
Closing: Students complete a "Word Wizard" to aid in defining what a unit fraction is and is not. See Appendix A for Word Wizard.
Activity # 4:
Learning Outcomes:
• Apply their understanding of fractions to solve Who am I puzzles.
• Communicate their reasoning while solving puzzles.
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using
area and number line, 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 principal to recognize and generate equivalent 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 ½. 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. Introduce the class to puzzle 1: Puzzle 1: 1/4 1/2 3/4 4/4 5/4
Show the first clue to the puzzle: "I am more than one half." Which of these fractions does this clue help us eliminate? 1/4 and 1/2. Discuss with the class why this clue helps us determine which choices to eliminate.
Show the second clue to the puzzle: "My denominator is larger than my numerator." How does this help us get closer to the answer? This will eliminate the fractions 5/4 and 4/4, leaving us 3/4 and 4/4. Show the last clue: "My answer is in simplest form"
Explore 22-25 minutes
Students work in pairs or at stations to solve the remaining Fraction Puzzles. As the students are working, observe how the students are solving the puzzles. What are strategies that students use to get started? What clues do they not understand? When students are finished with the remaining puzzles, students are to attempt to write their own fraction puzzles in their math notebook. Choose any five fractions, and write clues that will help eliminate a fraction or two at a time, but keep the others. See if other classmates are able to solve their puzzles.
Explain 20 minutes
As a class discuss how students were able to solve the puzzles. What clues were most helpful, and what clues were least helpful? Which clues did students need help with?
Share some of the puzzles that the students made.
If time permits, work as a class to solve a few of the puzzles that students have created
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