Fraction Five ~ Third Grade. Laying the Foundation for a Conceptual Understanding of Fractions. Third Grade CCSS 3.NF

Transcription

1 Fraction Five ~ Third Grade Laying the Foundation for a Conceptual Understanding of Fractions Third Grade

2 FRACTION FIVE RATIONAL Fractions present a considerable challenge to most kids. The lack of developmental understanding of fractions sometimes forces students to give up and resort to rules. However, if a firm fractional foundation is built, students stand a greater chance of understanding. This is a three month precursor to the 3 rd grade fraction standards. The questions laid out in this activity are meant for pre-teaching purposes. It is called Fraction Five because it is meant to be about 5 minutes of conceptual fraction discussion/understanding, daily. The questions continually ask students to make sense of the numerator and denominator. This part to whole relationship is vital for students to understand. Through these discussions, teachers are able to formatively assess their students understanding of the part to whole relationship. By starting to have these discussions with students about fractions early and frequently, throughout the beginning year, students are ready to conceptually understand more easily, when direct instruction begins. The questions can be copied for each student or displayed on the board each morning. These questions are not meant for grading purposes. They are intended to foster rich discussions and to be used as a formative assessment, to enable teachers to plan accordingly, to their students level of understanding and depth of knowledge of the foundations of fractions.

3 Daily Fraction Five 3rd Grade September 1. There are 14 students in our class today. 3 of them brought their lunch. Is that just a few, about half, or almost all of them? 2. You have spent one hour in your room cleaning. You have cleaned ¼ of your room. Have you about finished? 3. Draw a square and shade ½. Explain. 4. Shade ¼ of the figure below. Explain your answer. 5. There are students in our class today. of them have shorts on. Is that just a few, about half, or almost all of them? 6. Jackson was so proud that he read 3/4 of his book. Was he almost finished or just beginning? Explain your answer. 7. There are students in our class today. of them have sisters. Is that just a few, about half, or almost all of them? 8. I rode 2/4 of the rides at the theme park. Did I ride most of the rides or just a few?

4 9. Had you rather have ¼ of a cake or ½ of a cake? Explain. 10. There are students in our class today. of them have brown hair. Is that just a few, about half, or almost all of them? 11. Would you rather have 1/6 of a pizza or 1/3 of a pizza? Explain your answer. 12. A cake is cut into eighths. Three pieces are eaten. How much of the cake is left? Is this more than half or less than half? 13. There are students in our class today. of them are boys. Is that just a few, about half, or almost all of them? 14. There are students in our class today. of them are girls. Is that just a few, about half, or almost all of them? 15. There are 10 sweaters on a rack in the department store. 2 of the sweaters have stripes. What fraction of the sweaters has stripes? Explain why. 16. There are students in our class today. of them have shorts on. Is that just a few, about half, or almost all of them?

5 17. There are students in our class today. of them have blue eyes. Is that just a few, about half, or almost all of them? 18. A pie is cut into 5 equal pieces. All but one piece is eaten. What fraction of the pie is left? Is this more than half or less than half? students went to the zoo. 2 of them saw the penguins. What fraction of the students saw the penguins? Explain why. 20. Gaspar went to a party where there were 3 guests. 2 of the guests got a whistle as a party favor. What fraction of the guests got a whistle?

6 Answers: 1. Focus on these benchmark numbers. Is this number closer to one, half or zero? Students should have the knowledge to determine which is greater by reasoning about size. 2. ¼ is just beginning to clean. I know that one half is equivalent to 2/4 so ¼ is less than one half. 3. 1/2 4. Allow students to be flexible with their drawings. As long as they have 4 equal parts then they are correct. 5. For questions 5-14, you are focusing on determining if a fraction is closer to zero, half or one. Focus on the relationship of the numerator and denominator. Use your whole class as the denominator and just those that have on shorts as the numerator. Ask students how many more it would take to make a whole. Use benchmark numbers to determine if it s closer to zero, half or one out of 10 have strips so the fraction is 2/10. You may want to start talking about equivalent fractions here. You can draw a model to show that 2/10 and 1/5 are equal And 17 are like problems /5 less than half. It may be helpful to use a number line and show all 5 fifths out of 4 or 2/4 or ½ saw penguins. Again, use a number line out of 3 or 2/3

7 Daily Fraction Five 3rd Grade October 1. Decompose 1 into thirds. Draw those on a number line. 2. Draw a rectangle and divide it in to thirds and label each part. 3. (Teacher) Draw a number line on the board and place dots for thirds between 0 and 1. Have students label the dot that represents 2/3. 4. Which is the greater fraction ¼ or 1/8? 5. Which is the larger fraction 1/6 or ½? (Discuss that there is one piece of each and then reinforce the size of the pieces.) 6. Draw a number line on the board and place the dots for fourths between zero and one. Have students label the dots. 7. Which is the larger fraction ¼ or 1/6? Explain your answer. 8. Draw a rectangle and divide it into fourths. Label each part. 9. Which is greater ½ or 1/8? Explain.

8 10. Draw a number line and label 0 to 1 in sixths. (Pay particular attention to 3/6 being half way between 0 and 1. Associate 3/6 and ½) 11. Does this represent ¼? If so, explain how and why. 12. Does this represent ¼? If so, explain how and why. 13. Does this represent ¼? If so, explain how and why. 14. Does this represent ¼? If so, explain how and why.

9 15. Does this represent ¼? If so, explain how and why. 16. Draw your own model of ¼ and explain in words. 17. Partition a rectangle into sixths. Explain your drawing. 18. Name the fraction for each unit. Which fraction is larger? 19. What is one-fourth of a dollar? How do you know? (Discuss why we call them quarters. 20. Thinking about yesterday, a fourth of a dollar is 25 cents. What is a fourth of 100 dollars?.

10 Answers: 1. 1/3, 2/3, 3/3 on a number line 2. 1/3 2/3 3/3 3. 1/3, 2/3, 3/3 on a number line, pointing out 2/3. 4. ¼ (Discuss with students that there is one piece of both of them and the fourths are larger pieces than eights) 5. ½ (Discuss that there is one piece of each and then reinforce the size of the pieces.) 6. Draw a number line on your board and discuss fourths. 7. ¼ is the larger fraction. There is one piece of both. The fourth piece is larger than then sixth piece. When one whole is divided into fourths, those pieces are larger than that same whole divided into sixths ½ is larger than 1/8. There is one part of both of them and halves are larger than eights. 10. Draw a number line and label 0 to 1 in sixths. (Pay particular attention to 3/6 being half way between 0 and 1. Associate 3/6 and ½) 11. Yes, one part out of four is shaded and the parts are equivalent. 12. Yes, one part out of four is shaded and the parts are equivalent 13. Yes, if I combine both triangles, the make a square that forms ¼ of the shape. 14. Yes, if I move one shape over to create one long shape, then I have shaded in ¼ of the rectangle. 15. Yes, there are 4 squares shaded. If I moved them around I could create one long shape which is one fourth. I can also count the blocks and color them in to see the one-fourth piece. 16. Encourage students to draw their own representation of ¼. 17. ¼ 2/4 ¾ 4/4

11 Encourage students to think beyond the traditional picture of sixths. Expand on problems for your basis. 18. Emphasize that the size of the unit matters. Have students talk about the red fourth looks larger than the green half, but we can t compare these as fractions because the area units are not the same. It is not about the unit itself, we are thinking about area of the unit in this case. 19. One quarter. 4 quarters made up a dollar. ¼ is called a quarter dollars. 4 sets of 25 dollars make up 100 dollars. So a quarter is 1 part out of 4 parts.

12 Daily Fraction Five 3rd Grade November 1. What fraction of the figure is shaded? Explain your answer. 2. What fraction of the figure is shaded? Explain your answer. 3. Draw a square and divide it into fourths. Shade one half. Explain your drawing. 4. Shade 1/3 of the figure below. Explain your answer. 5. There are students in our class today. of them did their homework. Name the fraction. Is that just a few, about half, or almost all of them? 6. Robin ate ¾ of her sandwich. Is she just beginning or almost finished. Explain. 7. There are students in our class today. of them have brown hair. Name the fraction. Is that just a few, about half, or almost all of them?

13 8. Draw a number line and divide it into fourths. Label each section. Is there another fraction that is equivalent to 2/4? 9. Would you rather have 2/6 of a cake or 2/3 of a cake? Explain your answer. 10. There are students in our class today. of read a book last night. Name the fraction. Is that just a few, about half, or almost all of them? 11. Would you rather have 4/5 of a pizza or 4/8 of a pizza? Explain your answer. 12. Draw a number line that shows 4/3 and label There are students in our class today. of them like chocolate. Is that just a few, about half, or almost all of them? 14. There are students in our class today. of them like baseball. Is that just a few, about half, or almost all of them? 15. There are students in our class today. of them completed their homework. Name the fraction. Is that just a few, about half, or

14 almost all of them? 16. Which is greater, 2/8 or 2/6? Explain your thinking. 17. If 8 cookies were shared with 4 students, how many cookies would each student get? Write a fraction for this problem. 18. If 9 cookies were shared with 3 students, how many cookies would each student get? Write the fraction for this problem. (9/3) 19. Label the number line for the fractions it represents students went to the mall. 2 of them bought something. What fraction of the students bought something at the mall? Explain. Did just a few or most of them buy something? Can you think of an equivalent fraction for this fraction?

15 Answers 1. ¼ of the figure is shaded. Have a discussion about shapes being divided into equal parts. How can this figure be divided into equal parts. Why is the answer not 1/3? 2. 3/6 or ½ of the boxes are shaded. Ask students if there if they can rearrange those shaded boxes to help them see that one half is shaded. 3. After they draw their box and shade ½ of the boxes, ask them if they can write an equivalent fraction. ½ = 2/4 4. Discuss with the students how to look at the equivalent fraction of 1/3 = 2/6. They can look at the figure as three boxes or 6 boxes. 5. Problems 5-7 Look at the relationship between the numerator and denominator. Even though these are fractions much larger than any they will see, stress the relationship between the numbers. Is it closer to zero, half or one? 8. Students are to draw the number line into fourths. Emphasize the importance of the equivalent fractions of ½ and 2/ /3 of the cake is the largest piece. The relationship of the numerator and denominator is the focus of this problem. 2/3 is over half is 2/6 is just below half. Have students establish where half is in 2/ Look at the relationship between the numerator and denominator. Even though these are fractions much larger than any they will see, stress the relationship between the numbers. Is it closer to zero, half or one? 11. 4/5 of the pizza is the largest piece. The relationship of the numerator and denominator is the focus of this problem. 4/5 is over half is 4/8 is half. 12. Students are labeling this number line past one. They need to understand that fractions can be expressed as improper fractions as well as mixed numbers. You may want to have them label on out in thirds. 1/3, 2/3, 3/3, 4/3, 5/3, 6/3 13. Problems Look at the relationship between the numerator and denominator. Even though these are fractions much larger than any they will see, stress the relationship between the numbers. Is it closer to zero, half or one? 16. 2/6 is greater. Because the numerator is the same, you have two pieces of each fraction. We must look to see which fraction as the bigger pieces. Sixths are bigger than eights. So, because we have two pieces of each and the sixth pieces are bigger, 2/6 is the greater fraction. 17. Problems Emphasize in this problem how all fractions are division problems. 8/4 or 9/3 The students can draw a picture and give those cookies out to represent this problem.

16 19. ¼, 2/4, ¾, 4/4 or 1. 5/4, 6/4 Practice in going beyond one helps the students to have flexibility in the way they see fractions. 20. Because of the way this problem is worded, it may be hard for some students. Emphasize that a fraction is part to whole. What is the whole in this problem? 6 students. The part or the numerator is those students who bought something. So 2 out of 6 students bought something at the mall. The fraction is 2/6