Essential Strategy 8. Provide students with multiple strategies for comparing and reasoning about fractions.

Specific Strategies

There are a number of ways that students can be taught to compare fractions. The two strategies below emphasize developing the ability to reason about the size of the fraction and to solve fractions comparison problems without the need for pencil and paper.

#1: Comparing fractions to benchmarks such as zero, one-half and one

Tool Example: Estimating on a Number Line

The Estimating on a Number line tool allows the teacher to present students with a fraction and three benchmark numbers. The teacher can begin with one fraction as show below or require students to estimate the sums or differences to addition or subtraction problems as shown in the second example.

Estimating on a Number Line

Estimating on a Number Line

#2: Finding a Common Denominator

Tool Example: Finding Common Denominators

The Finding Common Denominator tool assists students in developing a conceptual understanding of what it means to find common denominators as well the procedural steps. Teacher can choose to begin with the models only by hiding the fraction numbers and equations.

Finding Common Denominators

#3: More or Less than ½ Modified

Tool Example: Order Fractions on a Number Line

Using the Order Fractions on a Number Line tool, the teacher can begin the lesson by presenting the number line without any tick marks along with some fractions that students will place on the number line. To help students see equivalencies, students use the arrows to the right and left of the number line to add or remove partitioning lines (ticks) to place equivalent fractions. Once the fractions are placed on the number line the teacher can guide student learning by having them compare the denominators of the equivalent fractions, identify those that are less than ½ and those that are greater than ½.

More or Less than ½ using Order Fractions on a Number Line tool

Classroom Activities

Below are some examples of how the tools can be used to create some of the sample activities from the book that are designed to help students compare and order fractions.

Activity 1: Put in Order

Tool: Order Fractions on a Number Line

The Order Fractions on a Number Line tool can be used to order fractions as an extension to the Put in Order activity. Students can work as a class with guided questions from the teacher to place the fractions. Questions such as “What number is half the denominator?” and others from the book can help students see relationships and compare fractions.

Put in Order activity using Order Fractions on a Number Line

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