As we begin fractions, I believe it is very important for students to practice counting fractions on a number line. I use a large number line on my whiteboard throughout the year, but this can also be done as projected activity, or if students are adept with number lines, on an individual whiteboard.
The number line is marked with zero and one at opposite ends, and I think it is important to do this in front of students - mark off different tick marks for different unit fractions including fourths, eighths, and halves. I begin with marking 1/2. Then model being very deliberate in determining where, and mark the fourth marks for 1/4 and 3/4.
To help my students determine the fractional amount, I first have them count the tick marks on the number line including one, to find the denominator. We discuss the number line is marked of in eight parts, or four parts, or whatever unit I am using to match the number line. The numerator is determined with counting.
It is also important to show students that each mark on the number line can represent more than one fraction. Counting fractions is an important step to the development of conceptual understanding.
During this lesson the students will each be creating a model of a unit fractions with halves, thirds, fourths, sixths, and eighths. These are the fractions listed in the Common Core Standards for third grade students, although it is also important for students to realize fractions exist in all units.
I model creating examples and non-examples by tracing a small book on white paper. I cut out two pieces and fold one to show fourths, and one to show four sections but not evenly folded. This second one creates the non-example of fourths. It is important students make this observation, so I suggest you pass it around and have students look closely and discuss what they see.
I also explain, "This is not fourths because each section is a different size from all the other sections." This explanation is important and it will be used by the students during independent work.
I chose a small book to trace because it is small enough to manage, and large enough to fold easily for the different fraction models. I explain to the students they will be using different items found by them in the classroom for each of the different unit fractions.
With a partner, students will create models of their choosing to show examples of each of the unit fractions along with a non-example to compare. Through the progressions with the standards for fractions students will be adding fractions with different denominators in fourth and fifth grade, and it is important for students to consider these different types of fractions.
Because we have created other equal unit fraction models at this point, some of this is review. The activity that is different for today's lesson is that students will be using items of their choosing of different sizes, tracing, and folding paper to show the unit fractions. They will use the same item to fold and create a non-example of the unit fraction.
For this lesson, students work with a partner This lesson gives the students practice working with unit fractions, precision, and problem solving to fold pieces of papers to create models. Some of the students with fine motor skills issues require assistance.
Students trace many different items in the classroom including small boxes and containers, tissue boxes, books, geoboards, and iPads. The only requirement is the item has to fit on an 8 1/2 by 11 sheet of paper.
The students trace the item two times, cut, and then create the unit fractions and non-examples of unit fractions on the same model.
If there is time (or early finishers) students are given the opportunity to create a display of their fractions using construction paper.
Closing the lesson, students share their work and examples with a partner. Students use the sentence stems:
This is an example because ________ .
This is a non-example because ___________.
I choose to use sentence stems so that students are focused on the math talk, explaining their thinking to another student. We are utilizing Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others - to communicate their reasoning to another student. Students are also expected to give each other feedback, and ask questions.