In the following technology applet, students can compare fractions using visuals and converting fractions into decimals. The number line also represents the fraction to show the magnitude of the number. One way to compare and order fraction is to use the relative size or the magnitude to reasonable compare. A second way is to find the decimal form by dividing the numerator by the denominator. Another way is to find common denominators and compare the fractions. In order to find equivalent fractions, students must understand the notion of renaming a fraction. Finding the equivalent fraction by multiplying the numerator and denominator by the same number may not mean much to students except a rule. For example, multiplying

But making conceptual connection to that procedure is to connect the idea that multiplying 3/3 is the same as 1.

Pattern blocks are great manipulatives to help students build conceptual and procedural understanding of shapes, proportions, equivalence, percentages, and fractions. The six standard pattern blocks include a yellow hexagon, a red trapezoid, a blue rhombus, a green triangle, a tan rhombus, and an orange square as shown below.

Except for one of the trapezoid bases, all the sides of the shapes are typically of the same length. Also, the areas of the hexagon, trapezoid, rhombus, and triangle are related through their area proportions. While the students can understand these relations by hands-on approaches, it is also helpful to have them discover these relations via technology-enhanced tools. For instance, the following tool provides an opportunity for students to select one of the six shapes in one dropdown box and another one in the other dropdown box and study the relationship between the two. The students have the opportunity to guess their answer before they press the “check answer” tab, which helps them to learn by discovery as follows:

One may also consider asking the relationship to illustrate part of a whole as follows.

To discover the relationships between the other pattern blocks, go to the website: http://completecenter.gmu.edu/java/patternblockactivity/index.html.

MORE RELATED RICH PROBLEMS TO EXPLORE

Think about it!

Describe how productive struggle can benefit students?

What classroom norms or routines can you establish in your classroom to nurture perseverance through productive struggle in your classroom?

Math Modeling Task Paint Color Palette

The Task

You will be creating a new paint color palette for your room. Experiment creating various shades of color using different ratios of 2 different food dyes. C reate 5 variations of color, using different amounts of both dyes in 5 different cups. Keep track of your drops in order to document your results and make them reproducible. Name for that color and provide a clear explanation as to why this is the PERFECT name for this shade. Finally make list of 3 different equivalent ratios that would work to recreate this perfect new shade.

Big Ideas

Analyze ratios and proportional relationships and use them to solve real-world and mathematical problems.