Fractions on a Number Line Lesson Ideas: The Pearl Diver Game
Grade Levels: 3-5, 6-8
In these number line lesson ideas which are adaptable for grades 3-8, students play an online math game to practice identifying, comparing, and ordering fractions on a number line.
Lesson Plan Common Core State Standards Alignments
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
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.
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.
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.
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
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.
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.
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.
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.
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.
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.
- Develop understandings of numbers, ways of representing numbers, and number systems.
- Understand and represent commonly used fractions.
- Apply understandings of fractions as part of unit wholes and as locations on number lines.
- Compare and order fractions on a number line.
- Computers with internet access for BrainPOP
Preparation:This lesson plan uses a free online math game by NMSU called Pearl Diver. The game starts out with simple numbers but quickly introduces more complex concepts, including negative numbers, fractions, and decimals. In between rounds, students will take a break from diving and practice estimating skills as they prepare to slice some electric eel sushi. Pearl Diver teaches number properties, plotting numbers, visualizing quantity on the number line, ordering numbers, and using the number line as a visual model for mathematical operations.
To play, students must dive at the indicated spot on the number line, which will allow them to discover a pearl. Use the mouse to move left and right. Click to dive, then click repeatedly to open the shell. At each level, you must collect four pearls before time runs out. If you collide with the electric eel, you lose one of your divers. In the sushi bonus round, slice the eel as accurately as you can, according to the directions.
You can find additional lesson resources (including bonus activities) on the Math Snacks website.
- Here are some ideas for incorporating the Pearl Diver Game into your class' instruction:
- Play the game as a whole class. Begin by playing the game yourself and using think-alouds to model mathematical practices. Then have student volunteers model various strategies and explain their thinking aloud, as well.
- Play the game as part of your small group math instruction. You can differentiate for students' needs by selecting the appropriate level of game play for each group. Students can take turns coming up to the interactive whiteboard or computer and explain the move they think is correct. Ask other group members to use a hand signal to indicate whether or not they agree. Allow students to explore the game in pairs. Encourage students to problem solve together and take turns.
- Provide time in class for students to play the game independently. Challenge students to advance through as many levels as possible in the allotted time. This is a great strategy to use after students have already had time to learn the basics of the game through group or partner play.
- Encourage students to play the game at home. All of BrainPOP's GameUp resources can be access by students on any computer with internet access, with no login required. Students can also download the free Pearl Diver app and play on their mobile devices. You can offer extra credit to any student who completes the entire game and submits a screenshot to you.