Dilate by a scale factor of 2 algebraically using the ordered pairs. This is a great opportunity to talk to students about scaling the axes of the graph and to make sure they understand how changing the scale to something other than one will need to be considered when finding the rate of change on the line. Sketch the ramp as viewed from the side on graph paper below. Use your rule to determine the number of blocks in Stage f. Consider the relationship between the number of years from now and the number of students enrolled. No, there is not a constant ratio and the line does not go through the origin. Complete the remaining 3 representations.
Graph and write equations for a proportional relationship and identify the proportional constant or unit rate given a table, equation, or contextual situation. Label each line with the candy it represents. Finding Slope from a Context g Homework: Why or why not. Describe in your own words what a linear relationship is composed of.
Stage 1 Stage 2 Stage 3 Teacher Note: I can also create a third representation for someone who makes more money than Addy and Rachel. Then order the constants from least to greatest by putting themselves in order.
They must abstract the given information pattfrn represent it symbolically as they develop and analyze the slope formula. The rate of change is in both problems; however in Hillary s savings the initial value is 0 and in the landscaping problem, the initial value is Consider the relationship between time in hours and amount of gas remaining in the tank.
Important vocabulary is reviewed below; perhaps have students add the words to a word wall or a vocabulary card.
2.2a homework connect the rule to the pattern
Create your own relationship. The graph for each truck is a straight line going through the origin. Renting the pavilion at the park for 3 hours costs 75 cents. This means that for every 1 cup of strawberries there are 1.
When cost is involved unit rate is often referred to as unit price. Unit rate is another way of interpreting the ratio s proportional constant. Hillary is saving money for college expenses. Show where you see the rate of change in your table. Students can title their context.
Chapter 2 – Student Workbook
The answer to question 1 how students drew the figure in stage 4 will help students to come up with a rule. Number of Papers Delivered c. While you discus the Rate of Change definition in the box above, you can show the Grace: The number of tennis balls is represented by the y values so if you substitute 0 in for y into your equation and solve for x you get 10 weeks. Finding Slope from Graphs d Homework: Consider the relationship between the number of years from now and the number of students enrolled.
She picks three girls for every boy.
Students should come with an understanding of what a unit 2.2s is and how to compute it. Answers will vary thhe on the initial context 8WB Create the additional representations table, graph, equation, context, geometric model of a linear relationship when given one representation and make connections between them.
Determine the rate of change the number of hot dogs consumed per minute for each boy. If using a bottle, the water level in the bottle should be parallel to the side of the bottle.
j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b – PDF
If you recieved 36 Euro, how many dollars did you exchange? Ask students to explain how Modeling with Mathematics is shown in this problem. When doing this, it saves a lot of time to have the pattern drawn up on chart paper several times so that students don t waste time drawing the pattern. They begin to see a pathern relationship as a special subset of a linear relationship where the rate of change is a proportional constant or unit pxttern and the graph of the relationship is a line that goes through the origin.
2.3j Class Activity: Use Dilations and Proportionality to Derive the Equation y = mx + b
The cat ran away from the milk at a rate of 4 feet per second. This will come out after slope is more formally introduced. It is an asset to include information such as membership in professional associations.