Sketch a graph for the four stories from number 1 above which you didn t choose in the space provided. I do not know how to make a third representation for someone who makes more money than Addy and Rachel. When building a staircase these measurements are chosen carefully to prevent the stairs from being too steep, and to get you to where you need to go. How did you draw your figure in stage 5 explain or show on the picture how you see the pattern growing from one stage to the next? Carmen is making homemade root beer for an upcoming charity fundraiser.
Or Callie delivers 2 papers for every dollar she makes. You may also want to include that it is a first degree equation depending on where students are at with grasping the general form. Graph and connect the ordered pairs 0,0 , 0,4 , 3, 0 , and 3,4. After this chapter students continue to work with linear relationships and begin work with functions. Complete the table below to show the relationship of boys to girls on Julie s team. If you want to discuss a negative slope on number 10 you can.
Using the same coordinate plane, draw a line that represents Charlie s earnings if x represents the number of hours worked and y represents the amount of money earned. Show how your rule relates to the pattern geometric model. Ask students to explain how Modeling with Mathematics is shown in this problem. Stage 0 It is the number of blocks in stage 0 the number of blocks the pattern starts with.
Monitor students while they are coming up with rules and ask a few students with different rules to present. Order the five activities from highest cost to lowest cost per hour. In other words our desired outcome y is obtained by starting with an initial value y-intercept and then adding our rate of change times x. Relxtionships the Prooportional to the Pattern 1. Label and sketch the base and height, for example: Connect the Rule to the Pattern b Class Activity: How would this change affect the graph?
Write an equation for the number of gallons g that will be in the pool after m minutes.
Stage 1 Stage 2 Stage 3 Teacher Note: Landon exhibits a proportional relationship because there is a proportional constant 2. The problems given below will help you to review how ratio and proportion can help relate and represent mathematical quantities from a given situation.
Graph this relationship on the same coordinate plane as Agatha s line on the previous page. Students start by gaining a conceptual understanding of slope-intercept form, then arrive at it using deductive reasoning, and finally in the last few lessons, students 2.a1 it. Does the graph describe a proportional relationship? Is this pattern a linear pattern? They both get paid the same amount of money per bag of popcorn because their ohmework of change are the same.
Depending on the background knowledge of your students you may decide to skip some of the problems in this section. Be sure to discuss the proportionality of each graph. How did you draw your proportuonal in stage relatkonships explain or show on the picture how you see the pattern growing from one stage to the next?
Identify proportional relationships (practice) | Khan Academy
This work requires students to move fluently between the representations of a linear relationship and make connections between the representations. When doing this, it saves a lot of time to have the pattern drawn up on chart paper several times so that students proportiional t waste time drawing the pattern. I know how to find the unit rate for both Callie and Jeff and state what the unit rate is describing.
They are the same line. Express the proportional constant as a unit rate. That it relztionships in fact a special linear relationship. Sufficient Mastery 3 I can identify the rate of change and initial value in 4 of the representation s of a linear model.
2.3j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b
Start with 2 gallons of water in the pool 8WB No, the flower will eventually die or stop growing; otherwise it would get too big to support its weight. Prove that your pattern is relayionships using the representations geometric model, table, graph, and equation as evidence. The unit rate is 3 of a Euro per dollar.
Complete the table below to show the relationship of boys to girls on Julie s team. Finding Slope from Two Points e Homework: At each particular point the x values represent the time that has passed and the y values represent the distance the truck has traveled.