Prior to any instruction students take the pre-assessment (See appendix). The test is read out loud to students and they are encouraged to try their best. It is fine if they are not sure of the answers. The assessment does not count as a grade. It is solely used for the purpose of gauging what prior knowledge students have on the topic.
Anticipatory Set:
Students are asked about various experiences which they may have had that deal with fractions. For example: Have you ever had a sandwich that was cut down to middle? Who has ever had a slice of pizza? How many of you ever folded a card out of a sheet of paper? Students are informed that all of these things deal with fractions- which is the new topic we are beginning. The teacher has a discussion with students about the importance of fractions. They are something we deal with everyday. If we order a pizza for the class, we need to know about fractions in order the cut the pizza so that everyone gets the same size piece. It wouldn’t be fair if some students had really big pieces and other students had really small pieces. The teacher reads the book Fraction Fun by David A. Adler.
During Lesson (Modeling):
Students are told of the importance of the fraction ½ (the fraction being discussed today). Halves are especially important if you want to share something with one other person such as a pancake or in a card game where each person receives half of the deck. The teacher demonstrates what one-half is by showing fraction cake pieces (See Teaching Aids). Students are told that in order for something to be divided in half, it must have two equal parts. The teacher then shows a picture of a circle. Students are asked to think in their head of a way they might draw a line to cut the circle in half. The teacher shows students a correctly divided circle and explains why it demonstrates halves. Following this, the teacher shows several non examples. With each example the teacher tells students why it is a non-example (See appendix). Re-iterate that in order for it to show halves it must be divided into two pieces and the pieces must be equal in size. Examples of circles divided in halves are shown with lines that are horizontal, vertical, and diagonal. Students are informed that the line may go in any direction as long as it is creating two parts, equal in size. In each example, the parts are labeled “1/2”.
Guided Practice (whole group):
The teacher places a sheet of paper on the DOCcam which contains numerous circles (see appendix). A story is told about the teacher’s family as follows:
Boys and girls, my family loves pizza. Sometimes we have pizza night and we order pizza for dinner, my dad and I really like cheese and pepperoni, but my mom likes vegetables better. Luckily, our pizza place makes half-and-half pizzas. So we order a pizza that is one half pepperoni and one half vegetable (peppers, onions, mushrooms). How could I make this circle look like the pizza we order?
Students give suggestions for how to draw the pizza while the teacher draws. If students make any incorrect suggestions for drawing the pizza, the teacher should explain the correct way and reiterate two equal parts- so everyone would think it was fair. Use of a ruler (straightedge) can aid in making straight lines. Students are asked what other kinds of half-and-half pizzas we might be able to make. These pizzas are added to the sheet. Pizzas should be drawn that include horizontal, vertical, and diagonal divisions. Students are asked if all of these pizzas can be considered half-and-half pizzas despite the difference in appearance (yes, as long as there are two parts, equal in size). If students have any difficulty with this concept, a circle is drawn and a line dividing it. The page is then rotated to demonstrate that at all locations there are still 2 equal parts.
Independent Practice:
Students are given the worksheet: Half-and-Half pizzas to complete on their own (appendix)
Assessment:
Students are assessed informally throughout the discussion during guided practice. They are assessed more formally through anecdotal notes during the independent practice portion.
Closure:
The teacher briefly reviews the learning for the day. When we split something in halves there are two parts that are equal in size.
Anticipatory Set:
The teacher reviews what was discussed in the class prior. Students watch a BrainPOP Jr. video titled Basic Parts of a Whole. The idea of part over whole (numerator/denominator) is briefly discussed upon completion of the video (to clarify students understood this). A subscripition is necessary to view this material.
During Lesson (Modeling):
Each student is given a post it note and asked to fold it in half in order to create 2 equal parts (halves). Students are encouraged to show another student the square and to ask themselves whether they each divided them the same way. The teacher calls on one pair of students and asks each student to show the class what they came up with. The teacher draws a picture of the square on the board and labels each side “1/2”. Following this, the rest of the class is asked whether they have folded their paper in a different way. Each different division is shared and drawn on the front board. It is expected that most students will divide the shape with either a vertical or horizontal line. If no student has generated a paper divided diagonally, this is modeled for the class.
Guided Practice (whole group):
Once all four possible divisions are shown on the front board, students are asked what they notice. Attention will be drawn specifically to what each half looks like (rectangles, triangles). Students are asked to imagine starting a business as follows:
Imagine that our class is going to start a business. Our company will be called Half-and-Half Rugs. What do you think our company is going to make and sell? If we are going to be making half-and-half rugs, we are going to need to make a lot of different kinds of rugs. We wouldn’t make much money if we only sold one kind of rug. That means we’ll need to make rugs that are divided into rectangles and ones that are divided into triangles!
The worksheet titled Half-and-Half Rugs (see appendix) is then placed on the DOCcam. The teacher demonstrates to students how to create a ‘rug’. The steps are as follows:
Independent Practice:
Students are given the worksheet Half-and-Half Rugs (see appendix) and a bag of precut pieces in varying colors (triangles and squares). They are to create their own half-and-half rugs following the procedure.
Assessment:
Students are assessed through their ability to create the half-and-half rugs.
Closure:
The teacher brings students back together and has a brief discussion about the learning from today. The parts of fraction are specifically reviewed.
Anticipatory Set:
The teacher reviews what has been learned over the previous lessons by asking guiding questions about ½ (number of pieces, equal in size, part over whole, etc.). The teacher talks with students more about their “rug store”. Students may also be shown a real rug.
Yesterday we worked to make half and half rugs. What if our store wanted to make more money though? We would need to be able to make other types of rugs also! Today we are going to learn about the fraction “1/4”.
Using what we have learned about the parts of the fraction (numerator and denominator) students are encouraged to share their thought on what they think one-fourth means (bottom number is 4 which means 4 parts).
During Lesson (Modeling):
The teacher again brings out the fraction cake pieces (see Teaching Aids). Halves are briefly reviewed in order to set the stage for fourths.
When we were talking about halves we learned that when we cut a shape in half there are two equal parts or pieces. Those parts have to be exactly the same (show the half pieces). We call each piece a half. Each half-circle is one of two parts of the circle. If you put two half-circles together you have one whole circle.
The teacher then shows the fraction pieces for fourths.
If we cut a shape into four equal parts those pieces are called fourths or quarters. Each quarter-circle is a fourth of the circle or a quarter of the circle. If you put four quarter-circles together, you have one whole circle.
Students are shown both examples and non-examples of circle and squares divided into fourths and the teacher explains that to be fourths there must be four parts and they must all be the same size (See appendix).
Guided Practice:
Whole Group:
The teacher draws three possible divisions for squares on the front board. Students are asked what they notice. Attention is drawn specifically to what each of the fourths/quarters look like (squares, rectangles, triangles).
Independent:
Students complete the worksheets titled Area Rugs: Circles (see appendix) and Area Rugs: Squares (see appendix) . The teacher is available for help as needed.
Independent Practice:
Students create area rugs which represent fourths. They are given the worksheet Area Rugs: Squares (see appendix) and individually cut colored pieces for gluing. Students need to do at least one of each kind of division (squares, rectangles, and triangles). As students complete their rugs they are to work on the worksheet Fourths (see appendix). Students are encouraged to take their time with this assignment. Students are told they will also have time in the following day to work on these so there is no need to rush.
Assessment:
Student’s understanding is assessed through their ability to complete the activity pages accurately.
Closure:
Students are brought back together for a discussion. They are asked what it means to divide something in fourths. Learning is reviewed in this manner.
Anticipatory Set:
Students are briefed on our learning form the day prior. Some student work can be shown to the class. Students are also informed that they will be ‘displaying’ our rugs for our ‘store’. The teacher will place a poster at the front of the room for students to paste their rugs on. Pages from Jerry Pallotta’s The Hershey’s Milk Chocolate Fractions Book may be read.
During Lesson (Modeling):
The teacher informs the students that they are going to be comparing halves and fourths today. Two circles are drawn on the board- one divided in half and one in fourths. The teacher tells students both circles are the same size. The first one is divided in half and the second one in fourths. The teacher then labels each circle with the number of pieces and each of the parts with a fraction. Students are old to imagine the circles are their favorite pizza. They are allowed to eat only one piece. Students decide whether they would rather have one half or one fourth and why. The teacher and students have a discussion based around student’s decisions.
Guided Practice (whole group):
Each student is given a mini Hershey bar. Students are asked to draw their attention to the fact that there are four separate sections. Students then break the bar in half (two pieces on each side). Student’s attention is drawn to the idea that there are two pieces and each piece is the same size. Students are asked what fraction each piece represents (reminded of part over whole). After, the students divide each half in half again (four equal parts). Students again will count how many parts/pieces they have. They will be asked what fraction each of these parts represents. Students then group the four pieces into halves (two and two). This allows students to visualize the difference between a half and fourth. Students are then told they may eat either one half or one fourth. Students choose and then eat that fraction.
Independent Practice:
Students complete the worksheets entitled Identifying Halves and Fourths (see appendix)and Assessment: Halves and Fourths (see appendix). Students then continue to work on their rugs.
Assessment:
Student’s understanding is assessed through their ability to create rugs and also complete the independent practice worksheets accurately.
Closure:
Students are brought back together and are asked to turn to a partner and tell them one important thing you need to remember when you divide a shape into halves or parts. What is important about the parts? (They are the same size). Which is bigger ½ or ¼?
Following instruction students will be given a post-assessment (See appendix). Unlike the pre-assessment this assessment will count as the student’s final grade for the learning experience.
Students completing independent work early are allowed to play fraction games on the computer. During recess on Tuesday and Thursday we have a game day. During this time, students are able to play a series of fraction board games. These games include: