دليل المعلم Teacher Edition Course 1 الرياضيات Reveal الصف 6 منهج انجليزي الفصل الأول

دليل المعلم Teacher Edition Course 1 الرياضيات Reveal الصف السادس منهج انجليزي الفصل الأول

   Explore Compare Two Quantities

Objective

Students will use Web Sketchpad to explore how to maintain the same relationship between two quantities as one of the quantities changes

 Teaching the Mathematical Practices

 Reason Abstractly and Quantitatively As students discuss the Talk About It question on Slide 3, encourage them to discuss why or why not the bus moves if there are 2 teachers

Ideas for Use

Recommended Use Present the Inquiry Question, or have a student volunteer read it aloud. Have students work in pairs to complete the Explore activity on their devices. Pairs should discuss each of the Talk About It’ questions. Monitor student progress during the activity. Upon completion of the Explore activity, have student volunteers share their responses to the Inquiry Question

What if my students don’t have devices? You may choose to project the activity on a whiteboard. A printable worksheet for each Explore is available online. You may choose to print the worksheet so that individuals or pairs of students can use it to record their observations

Summary of Activity

Students will be presented with various scenarios of the number of students and teachers on different buses and determine how many additional students or teachers need to be added in order to maintain the relationship of 1 teacher for every 8 students

Inquiry Question

 How can you use reasoning to maintain the same relationship between two quantities as one of the quantities changes? Sample answer: As one of the quantities changes, I can reason about how the relationship between the quantities must remain the same. For example, if the relationship between students and teachers is 1 teacher for every 8 students, then if there are 24 students, that means there are 3 groups of 8 students, and each group needs a teacher chaperone. So, 3 teachers are needed

Go Online to find additional teaching notes and sample answers for the Talk About It! questions. A sample response for the Talk About It! question on Slide 3 is shown

Talk About It

SLIDE 3 Mathematical Discourse How many teachers did you place on the bus? Did the bus move? Why do you think the bus either moved or did not move? Sample answer: I placed two teachers on the bus and the bus moved, because the relationship 1 teacher for every 8 students is maintained. If there are 16 students, that is two groups of 8 students, and one teacher is needed to chaperone each group

Teaching Notes

Students will learn that using a ratio is another way to compare quantities. You may wish to have students move through the slides that show how the bar diagrams can be used to compare the number of cups of lemon juice to the total number of cups of lemonade as the number of batches increases. Ask students the following questions 

 Why is the number of sections representing lemon juice and lemonade the same for each bar diagram? Sample answer: By keeping the number of sections the same, I can be sure that the ratio relationship between the two quantities is maintained

Why does the number labeled inside each section increase for each batch? What does this number represent? Sample answer : The number labeled inside each section indicates the number of cups each section represents, whether or lemon juice or lemonade. As the number of batches increases, this number increases

Go Online to find a sample answer for the Talk About It! question on Slide 4

DIFFERENTIATE

Language Development Activity

 Have students practice using the phrases for every and for each when describing ratio relationships. Students may be unsure when to use for every and when to use for each. Bu may wish to point out that the phrase for every is used when the second quantity is plural, and for each is used when the second quantity is singular. Some examples are shown

For each cup of simple syrup, there are 2 cups of lemon juice

For every 2 cups of lemon juice, there are 7 cups of water

Knowing when to use each versus every can be confusing even among fluent English language speakers. Allow students space to make mistakes; the most important concept for them to grasp is the reasoning behind why these phrases are used when describing ratio relationships. Have students work with a partner to respond to the following questions, given the scenario presented in the Learn

Consider the phrase for every 2 cups of lemon juice, there are 10 cups of lemonade. Why do you think the phrase for every is necessary here? Sample answer: Without using for every, the relationship might not be maintained when making more batches of lemonade. By using for every, it is defining the connection between lemon juice and lemonade that persists for any number of batches

 Write your own sentences comparing the quantities in the recipe. that being with for every or for each. Sample answers given. For every 2 cups of lemon juice, there is 1 cup of simple syrup. For each cup of simple syrup, there are 7 cups of water

Explore Compare Two Quantities

(continued)  Teaching the Mathematical Practices

2 Reason Abstractly and Quantitatively Encourage students to use reasoning about the relationship between the number of teachers and students and what it means to maintain that relationship as the number of students or number of teachers changes. In order to maintain the relationship of 1 teacher for every 8 students, encourage them to think about groups of 8 students. If there are two groups of 8 students (16 students), then two teachers are needed. For every group of 8 students, one teacher is needed

Go Online to find additional teaching notes and sample answers for the Talk About It! questions. A sample response for the Talk About It! question on Slide 5 is shown

Talk About It

 Mathematical Discourse How many teachers did you place on the bus? Did the bus move ? Why do you think the bus either moved or did not move ? Sample answer: placed three additional teachers on the bus and the bus moved, because the relationship 1 teacher for every 8 students is maintained. If there are 32 students, that is four groups of 8 students, and one teacher is needed to chaperone each group. This is a total of four teacher chaperones