1 План урока Fractions on the Number Line Возрастная группа: 4 t h Grade, 5 t h Grade Texas - TEKS: G3.3.N O.B Riverside USD Scope and Sequence: 3.N F.2b [3.8], 4.N F.1 [4.6], 4.N F.2 [4.6] Oklahoma Academic Standards Mathematics: 3.N.3.2, 3.N.3.4, 4.N.2.1, 4.N.2.2, 4.N.2.8, 5.N.2.4 Virginia - Mathematics Standards of Learning (2009): 4.2a, 4.2b Common Core: 3.N F.A.2b, 4.N F.A.1, 4.N F.A.2 Mathematics Florida Standards (MAFS): 3.N F.1.2b, 4.N F.1.1, 4.N F.1.2 Alaska: 3.N F.2b, 3.N F.3 b, 4.N F.1, 4.N F.2 Minnesota: 4.1.2.1, 5.1.2.3, 5.1.2.4 Fairfax County Public Schools Program of Studies: 4.2.a.2, 4.2.a.3, 4.2.a.4, 4.2.a.5, 4.2.a.6, 4.2.b.1, 4.2.b.2 Nebraska Mathematics Standards: M A.3.1.1.g, M A.4.1.1.d, M A.4.1.1.i, M A.4.1.1.k, M A.4.1.2.e South Carolina: 4.N SF.1, 4.N SF.2 Indiana: 4.C.6, 4.N S.3, 4.N S.4 Georgia Standards of Excellence: M GSE 3.N F.2b, M GSE 4.N F.1, M GSE 4.N F.2 Virginia - Mathematics Standards of Learning (2016): 4.2.b Онлайн ресурсы: Al l t he Same t o M e Opening Teacher present s Students play Class discussion Closing 6 1 2 1 2 1 2 5
2 ЦЕЛИ: E xpe ri e nc e a visual model for equivalent fractions P rac t i c e identifying fractional portions Learn to compute equivalent fractions De vel o p algebra skills Ope ni ng 6 Ask the students to draw a figure that represents. A possible response: Ask one student to present her drawing to the class. How does this represent? A possible response: The entire rectangle represents one whole. The rectangle is divided into six equal pieces. Each piece is of the entire rectangle. Shading three of the pieces represents. What is another fraction we could use to describe the shaded region? How do you know? We could say that the shaded region represents. Half of the entire rectangle has been shaded. One half and are called e q ui val e nt f rac t i o ns. Equivalent fractions are fractions that have the same value, even though they may look different. They name the same part of the whole.
3 Display the following: Can we think of more than one way to name the portion that has been shaded? Three fourths and portion. are two different ways to name the shaded So and name the same part. They are equal. They are equivalent fractions. T e ac he r prese nt s Al l t he Same t o M e - F rac t i o ns o n t he N umbe r Li ne 12 Present Matific s episode Al l t he Same t o M e - F rac t i o ns o n t he N umbe r Li ne to the class, using the projector. The goal of the episode is to fill in the missing number(s) to make equivalent fractions. Example : Please read the instruction.
4 Students can read the instruction at the bottom of the screen. A number line has been divided into parts to help us solve this problem. Above the number line are small green dividers representing one way to partition the line. Below the number line there are small pink dividers representing another way to partition the line. You will notice that the green and pink dividers sometimes meet. This is where they are equivalent. Look at the blue pointer. It is pointing at the two equivalent fractions for this problem. What is the missing number in this problem? Students can answer based on the episode. Click on the to enter the number that the students indicate. If the answer is correct, the episode will proceed to a new problem. If the answer is incorrect, the instruction will wiggle. For the second problem, the episode will present dials. The dials will already be set to the denominators in the problem and the line will already be partitioned correctly. However, the pointer will not yet be in place. Where should we place the pointer on the number line? Move the pointer as the students indicate. Now we can answer the problem. What is the missing number? Students can answer based on the episode.
5 Click on the to enter the number that the students indicate. If the answer is correct, the episode will proceed to a new problem. If the answer is incorrect, the instruction will wiggle. For the rest of the problems, the dials will not be properly set. Each dial represents the de no mi nat o r of each fraction, or the number of partitions on the number line. You will need to turn the dial to adjust the partitions. Ask for students input in how to change the dials in order to solve the problems. The episode will present a total of six problems. St ude nt s pl ay Al l t he Same t o M e - F rac t i o ns o n t he N umbe r Li ne 12 Have the students play Al l t he Same t o M e - F rac t i o ns o n t he N umbe r Li ne on their personal devices. Depending on time, students may also proceed to the E q ui val e nt F rac t i o ns - F i ndi ng Unkno wns worksheets. Circulate, answering questions as necessary. Cl ass di sc ussi o n 12
6 Suppose the episode asked you to solve the dials?. How do you set The dials control the number of partitions on the number line. So each dial must be set to each denominator. So one dial should be set to five and the other to 15. Once you have the dials set at five and 15, how do you determine the answer? Look at the twelfth partition on the part of the line that is divided into fifteenths. Then find how many fifths meet up with. What is the answer for? Four is the missing number. Four fifths is equal to. Suppose the episode asked you to solve the dials?. How do you set One dial should be set to 16. Place the pointer on. Adjust the other dial until the fourth partition meets up with. Once you have the dials set, how do you determine the answer? The number on the second dial is the answer. What is the answer for? Eight is the missing number. Four eighths is equal to. Suppose the episode asked you to solve the dials?. How do you set Set the pink dial to any number greater than or equal to five. Place the pointer on the fifth pink partition. Adjust the green dial until the tenth green partition meets up with the fifth pink partition.
7 Once you have the dials set, how do you determine the answer? The numbers on each dial are the answers. What is the answer for? Responses may vary. A possible response: We can use six and 12 as the missing numbers. Five sixths is equal to. How many answers are there to the problem? There are infinite answers. You can set the first denominator to any number you want. Since it can be any number, there are infinite ways to do this. The first denominator determines the second. In this problem, the second denominator is always twice the first. For example, if the first denominator is six, then the second is 12, since 14, since.. If the first denominator is seven, then the second is Did anyone find a way to solve the equivalent fraction problem without using the dial? For example, how could we solve the problem? Responses may vary. Two possible responses: 1. In the fraction, the numera t o r is half the denominator. So that must be true in the other fraction as well. Half of 20 is 10. So the numerator is 10, and the fraction is. 2. The denominator in the first fraction is four and in the second fraction is 20. So the denominator has been multiplied by five. So we must also multiply the numerator by five. When we multiply two by five we get 10. So the numerator is 10, and the second fraction is. Complete the following problems:
8 Complete the following problems: Let s make a list. Write the following on the board: What patterns do you see? Responses may vary. A possible response: In the list for, the numerators increase by one each time and the denominators increase by two each time. In the list for, the numerators increase by four each time and the denominators increase by five each time. The original numerator determines what you count by for the numerator, and the original denominator determines what you count by for the denominator.
9 Cl o si ng 5 Define equivalent fractions. Equivalent fractions are fractions that have the same value. Hand out a small piece of paper. Ask the students to: 1. State two equivalent fractions. 2. Draw two figures that represent the fractions and demonstrate that they are equal. Collect the papers to review later. A possible response: