Fractions Lesson Plan: Satisfraction

Grade Levels: 3-5

In this lesson plan, adaptable for grades 3-5, students play Satisfraction, a game that challenges students to explore fractions by comparing fractional amounts.

Lesson Plan Common Core State Standards Alignments

Grade: 03

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.

Grade: 03

CCSS.Math.Content.3.NF.A.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Grade: 03

CCSS.Math.Content.3.NF.A.2a

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.

Grade: 03

CCSS.Math.Content.3.NF.A.2b

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: 03

CCSS.Math.Content.3.NF.A.3

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Grade: 03

CCSS.Math.Content.3.NF.A.3a

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Grade: 03

CCSS.Math.Content.3.NF.A.3b

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.

Grade: 03

CCSS.Math.Content.3.NF.A.3c

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.

Grade: 03

CCSS.Math.Content.3.NF.A.3d

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Grade: 04

CCSS.Math.Content.4.NF.A.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: 04

CCSS.Math.Content.4.NF.A.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: 04

CCSS.Math.Content.4.NF.B.3

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

Grade: 04

CCSS.Math.Content.4.NF.B.3a

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

Grade: 04

CCSS.Math.Content.4.NF.B.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.

Grade: 04

CCSS.Math.Content.4.NF.B.4

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

Grade: 04

CCSS.Math.Content.4.NF.B.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).

Grade: 04

CCSS.Math.Content.4.NF.B.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.)

Grade: 05

CCSS.Math.Content.5.NF.A.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Grade: 05

CCSS.Math.Content.5.NF.B.7a

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

Grade: K, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12

CCSS.Math.Practice.MP2

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Students will:

Use multiple visual representations (e.g. squares, number line and numerical fraction) to illustrate the relationships between parts of a whole
Recognize and generate simple equivalent fractions, and use a visual model to explain why these fractions are equivalent

Materials:

Computers or other devices with Internet access
Interactive whiteboard or other display

Preparation:

This lesson features a fraction game called Satisfraction, developed by Filament Games. The game invites players to apply their knowledge of fractions by slicing and slashing blocks into fractional parts.

Preview and play Satisfraction to plan how you will adapt it to your students’ needs, and consider at which level you’d like students to begin. The first four levels include tutorial overlays that remind players of the basic mathematical concepts they will need to understand in order to progress in the game.

If students will be working in small groups, review tips on Setting Cooperative Gaming Expectations.

Depending on your classroom routines and available technology, you may want to consider these grouping options:

1:1 with students and devices
Two to three students sharing one device and swapping ideas and the device back and forth
Station model where small groups rotate through using the devices

For ideas on how to use SnapThought with this game, read Satisfraction: SnapThought Prompts for more information and specific SnapThought prompts to provide students during game play.

Build background knowledge or reinforce topics with these BrainPOP movies: Reducing Fractions, Fractions, Proportions, Ratios, Division, and Multiplication.

Lesson Procedure:

Depending on your students’ familiarity with fractions, you may want to play one of the related BrainPOP movies, such as Reducing Fractions or Fractions on the whiteboard or other display.
Project Satisfraction on the whiteboard for the class to see. Explain to students that they will be using their knowledge of fractions to play this game.
Have students explore the first few levels of the game independently, in pairs, or small groups. Or they can begin at a level that you determine, which may be different for different students.
Circulate as students play, answering questions as needed. If students have individual logins through My BrainPOP, encourage them to use the SnapThought tool to take snapshots during game play, and reflect on their strategies. Review Satisfraction: SnapThought Prompts for suggested prompts.
After about ten minutes, pause the gameplay and have students come together for a whole-class discussion about the strategies that they used. They may share their SnapThought responses at this time. You may also ask additional questions such as the following:
- How did you know how many pieces to cut the blocks into?
- How did your slicing affect the number line?
- What happened as you“leveled-up”? What made higher levels more difficult?
Allow for another 10-15 minutes of gameplay, encouraging students to reflect on their previous strategies and try new ones as they level up. Emphasize that they can go back to earlier levels and try to look at them in different ways in order to help them with higher levels.

Extension Activities:

Challenge students to create basic word problems that could be represented using the blocks in one or more levels. For younger students, you might come up with a few word problems beforehand that can be applied to particular levels in order to guide their understanding and help them transfer their gameplay into real-world contexts.

Filed as: 3-5, CCSS.Math.Content.3.NF.A.1, CCSS.Math.Content.3.NF.A.2, CCSS.Math.Content.3.NF.A.2a, CCSS.Math.Content.3.NF.A.2b, CCSS.Math.Content.3.NF.A.3, CCSS.Math.Content.3.NF.A.3a, CCSS.Math.Content.3.NF.A.3b, CCSS.Math.Content.3.NF.A.3c, CCSS.Math.Content.3.NF.A.3d