I use this lesson for students to use nonstandard measurement to explore ratios using their own body.
I've created a PowerPoint to help you guide your students through this lesson.
Start by asking your students how many times do they think a piece of string equal to their height could be wrapped around their head like a headband. Let them discuss it with their groups. During this time you can be listening for their accuracy in estimation skills. When I do this I take a mental note of the students who have a misconception and I make sure I keep an eye on how they work through this lesson. I want them to discover for themselves their mistake, but it may take some guidance through questioning.
Model for your students by having a student help you cut a string that is your height and then wrap the string around your head - you may want to put in some safety instructions here or you may have students making poor choices when it is their turn.
Next pair students up and then ask them to cut the string to their height and figure out how many times they can wrap the string around their heads like a headband - again adding safety cautions.
I ask my students to do the experiment and then when they are done to sit with their partner, in a chair or on the ground, this way I know when they are finished.
Once they are done ask the questions:
Was it about 3 times? and emphasize the about.
We found out that our head is about 1/3 our height. You can write this as a ratio of 1:3.
head:height = 1/3
or head = 1
Next have your students discuss what they think the ratio is of everyones foot and their height. You may want to ask them to put their strings down because some will start to actually measure and you want them to be discussing their estimates.
Next ask them how they can find the ration between their foot and their height.
The ratio should be about 1/6 = foot to height or a ratio of 1:6.
Continue the exploration by telling your students that their foot and their forearm should be just about the same length - again emphasizing about. They can record this as foot to forearm = 1/1 or a ration of 1:1.
Next the fun exploration of ratio begins and you are going to hear excited children. I put up the following chart for my students to copy in their math journals.
Height Fraction Ratio
4. Upper arm
6. Lower leg
9. Arm span
Once again I have them sit down when they are done as a signal to me.
Here is where the students figure out there are common ratios. This starts in the PowerPoint on slide 5. Put your students into groups of 4 so they have a bigger number of ratios to compare. Ask them to find common ratios they have and to mark them with something such as a highlighter. They will be needing them for a class discussion.
As your students are doing this, you will find you do not have too much to do - they are engaged and exploring rations all on their own. Do listen for any misconceptions students may have about comparing the ratios, but I bet another student will clear it up for them.
Student reflection creates a more than an 80 percent retention rate when combined with discussion. Slide number 7 of the PowerPoint is title Reflection 1, 2, 3. When I am creating reflection questions for my students I always use the same categories for the three questions. The first is specifically about the content in the lesson, the second is a social question about group work - typically pointing out the positive aspects or it can be a critical thinking question - one where students are reflecting on their own thinking. or metacognition. The last is a personal question focusing on behavior.
This part of the lesson is the most often missed because we run out of time but it almost is the most critical because it cements what is learned. To help myself remember reflection I have a symbol up in my room - a pelican. This came from a Tribes training many years ago and the pelican's name is Reflection. She soars over the class looking down on us reminding us to reflect on our learning and behavior.
I always use this extension because it doesn't take much time, students can positively identify with other students, and it is one more comparison with numbers.
have your students compare their heights with their outspread arms. A typical adult will have the same measurement for arm span and height but not kids. They are all growing differently. There will be kids who are just like the adults, they have equal measurements. I call them the squares. There are kids who will have a wider arm span than their heights - they are the wide rectangles; and then there are the kids who have a shorter arm span than their height. The are the tall rectangles.
Have each of your students write their name in the corresponding box. I use a Smartboard for this but it would be a great poster to keep up in the room.
Again don't forget to reflect! This one can be more social to build a more collaborative classroom community.