For 4/4 - Response to Chapter 18
Make up a realistic proportional situation that can be solved mentally by a scale-factor approach and another that can be solved mentally by a unit-rate approach. Explain why you think these situations would be good ones to use with students?
To teach about unit-rate approach, ask students to determine how long it takes them to read five pages of their text book. Give them stopwatches, and have them begin the reading (making sure to let them know it’s not about speed; reading to understanding is much more important). Have them make a chart or table. Ask them how long it would take them to read ten pages, 20 pages, 50 pages, 100 pages, etc. Ask them to determine what their reading rate is, so that they can plan out how much to read per night to get their reading assignment done by the end of the week. How many pages will they need to read each night if there are 100 pages in the text? How long will that take them?
ReplyDeleteThis would be helpful for students because it would teach them about time management, and help them designate enough time each night for homework.
To teach students about the scale-factor approach, have them look at a map of the United States. Ask students to estimate the distance from our school to NYC and to Denver, CO, for example, by using the distance scale key provided on the following map:
https://www.lib.utexas.edu/maps/americas/unitedstates_ref802634_1999.pdf. (Anyone know how to add a link in this forum? I don't, but if you want to check it out, you could cut and paste it in your browser. It's just a basic map with scale key, 1 inch per 5 miles).
Ask students to create a table with both the values in inches from the distance scale key and the estimated miles to each place. If an inch equals 5 miles, how many miles would they have to travel to get to the city or state they most want to visit?
This would be a way to show students where we are in terms of the country’s geography, and it would be fun to pretend to be able to go anywhere. I wonder where students would want to go?
Meg, in the unit-rate I do not see asking the students how many pages they read in one minute or how long it takes to read one page. So although we can call a unit a lot of things, I usually think of unit rate as how much for one or in this case in one minute how much can you read. I use the example you used with my students to plan how long it will take to finish their homework reading assignment and we time for a minute and then divide the number of pages into the total they have to read for the night.
ReplyDeleteFor unit rate I will ask the students if the grocery store rate is 11 candies for $2.75, how much it is for one candy. I ask the students how many quarters are in a $1., $2. and finally $2.75. The students learn that 11 goes into 2.75 evenly and that one candy will cost .25 cents.
Giving the students graph paper, I ask the students to draw a polygon that represents their room at home. Then I ask the students for homework to measure their room. The next day the students need to tell me what value each 1/4 inch square on the graph paper equaled if their drawing represents the actual room. Then we make a key to represent the scale of each block to represent the actual measurement of their room. It is usually interesting to see how many students decide to redraw their original room drawing.
Thanks for your comment, I see what you mean! ~Meg
DeleteWe need to purchase 20 trowels for our class garden project. 10 trowels cost $40 dollars. How much would we need to spend for 20 trowels? How much does each trowel cost? If the store was having a two for one special, what would we spend for our purchase? I would give this problem to students when they are just beginning to conceptually understand solving proportional situations using the unit-rate. This problem is simple to calculate and easy to visualize the division.
ReplyDeleteContinuing with our garden project, I would ask students to measure out a garden plot using blocks on graph paper. The students would be asked to figure out the area of the garden plot they've created. Then I would ask them to consider having to double the size of the plot for a larger garden project or half the plot size for a smaller project. Students would need to use the scale factor method to scale up and scale down these area sizes. Similarly to mernickg, students would create real size value of their gardens by determining the value of each 1/4 inch square. Students would then be able to determine actual size of their three plots.
Samantha is having her 13th birthday party.
ReplyDeleteUnit Rate
Samantha bought 24 cupcakes for $40.68. At the same price, how much would 30 cupcakes cost?
Scale Factor
Samantha bought 12 cupcakes for $20.34. How much would 3 dozen cupcakes cost?
I think this is a good example to use with students because when planning a party for friends you need to take into consideration the amount and cost of the products, like cupcakes, needed to ensure their is enough for everyone. This is a scenario that I think most children will be familiar with and can easily be adapted to include other items and prices.
Hi like how you are using a broad subject like sports so students would be able to think if their own problems based on their interests.
ReplyDeleteUnit Rate Approach
ReplyDeleteOn Saturday, Sam bought pizza for his baseball team after the game. He paid $36 for 3 pizzas. There wasn't enough pizza, for this week he plans on buying 4 pizzas. How much should he expect to pay, assuming he buys the same kinds of pizza?
The baker needs to mix bread dough for the following day. One recipe, which makes 3 loaves, calls for 36 oz. of flour and 24 oz. of water. How much flour does he need if he wants to mix enough dough for 12 loaves? 13 loaves (extension)?
Students can demonstrate their understanding of unit-rate problems by creating a table that represents how long it takes to get to different places in their town if they travel at a constant rate. Students can create a table that has the given rate (ex: 25mph) and fill in the distance from school to: the grocery store, home, a local park, the next town over. With this information students can then use the unit-rate method to determine how long it takes to get to each of these locations traveling at 25 mph. This is a realistic situation that many students can relate to and formulate new questions from, how long will it take if we are traveling 30 mph, 35 etc. How long will it take to go 20 miles at 43mph?
ReplyDeleteI also like the idea of using maps to help students develop their understanding of the scale-factor. Students can start by looking at a map of their town or city and use a smaller scale (1 inch = 5 miles) to see how far their home or other places are from school. Students can then look at a map of their state and see how the scale changes (1 inch = 30 miles) and see how far the capital of their state is from school. They can continue to expand looking at maps on a larger scale (the United States, North America, the world) and see how far away different places are from their school.