Measurement in a Real World Setting

Context:
Renee teaches in a GED prep program in an urban, community-based learning center. Helping her students understand the importance of learning anything other than what they directly need to pass the GED test is a continual struggle. EFF has helped her students begin to see the value of learning to apply what they learn to real life situations. One opportunity to combine learning a skill needed for the GED (measurement) with a real world purpose came about after there was a fire in the learning center. The class would be moving to a new space - one that would need painting and new furniture. Renee suggested that they could work on their math skills by measuring the room to see what furniture would fit and to calculate how much paint they would need. After talking it over, the class agreed to help .

The class was already familiar with EFF Framework. They decided to look first at the Common Activities and decided Gather, Analyze and Use Information best fit their goal. Then they looked at the Standards Wheel. Everyone readily agreed that Use Math to Solve Problems and Communicate was the Standard they needed for this project and, with Renee’s help, they then looked at the Standard to see how it could guide their work.

Use Math to Solve Problems and Communicate
How we will address the Standard
Work with pictures, numbers, and symbolic information We will :
• use a measuring tape-feet,   yards,  inches

• for paint—gallons and quarts
  use a calculator
Apply knowledge of math to figure out how solve a problem and carry out a task • figure out how to decide what     furniture will fit and how much paint   to buy
Define and select data to be used • decide which measurements to use   for each task
Determine the degree of precision required • measure precisely so we don’t buy   too much paint; have room for   furniture

• make a scale drawing of the room
Solve and check the problem using math • use calculator

• solve and check all the math   problems
Show the results using graphs, charts, tables, or algebraic models • give the results to the program   director so she can buy what we   need.

They decided to work in two teams to solve the same problems. That way they could check each other’s work. They also wrote a clear statement of their goal:

Our class will learn how to measure our new classroom and make a precise scale drawing. We will calculate how much paint the program will need to buy and what furniture will fit in the room.

Next Renee worked with the class to figure out what they already knew related to this goal and what they needed to learn. She looked at their GED practice test results to see who already knew basic measurement calculations. Then, at break time, she did a short one-to-one interview with each student. She learned, for example, that Mary had never used a tape measure or made a scale drawing. She knew the formulas but only in a classroom context. Jan had painted, but while painting her mother’s house, she had to go get more paint three times in one day! Joseph has painted and bought furniture for his home many times but didn’t know what a scale drawing was or how it might help him. None of the students had thought of using a calculator to help with the kind of math in this project. After the break, Renee helped them brainstormed a learning list of what good performance on their task might entail.

To perform this goal well we will need to:
  • know how to measure inches, feet, yards, quarts and gallons
  • know how to determine when we need to use formulas for perimeter and area
  • make a scale drawing using graph paper and explain how we used math to make it
  • calculate the area of a room and determine how much paint is needed
  • check our work for precision
  • communicate this information in a report to the program director
Next, the class worked on a learning plan. It included:

Day 1: (90 minutes—in our temporary classroom)
Practice measuring length and width and calculating perimeter and area
Make practice scale drawings on graph paper
Use sample paint cans-quarts and gallons to practice figuring out how much paint is needed for different sized rooms.

Day 2: (90 minutes—in the new classroom)
(In two teams) Measure the room, including windows and doors. Make a scale drawing. Calculate how much paint will be needed. Look through furniture books. Create paste on “furniture” to scale and arrange them on the scale drawing. Compare results with the other team.

Day 3: (90 minutes—in temporary classroom)
Check each other’s work. Work on a final finished room plan to give the program director. Each team will share their plan with the whole group.

Renee was aware of the importance of weaving assessment into on-going classroom activities, so she asked students to think about how they would assess their learning related to the standard along the way. They filled in the chart below.

After some of the group started to complain that the activities were getting them off track in preparing for the GED, Renee asked if they would like her to give them sample story problems on measurement from the GED practice book as another check on what they had learned. They agreed to add this to the plan.

How Can We Learn It?
How Will We Show We Know It?
Day 1:
Measure length, width with a tape measure; calculate area using calculator.
Figure out paint needed by using can
Make a scale drawing
- Give each other sample   measurement problems to work on
- Do some homework problems
- Make a scale drawing (each make 1)
Day 2:
Make a scale drawing of the new classroom
Determine if it is accurate
- Each team will show their scale   drawing and explain how they used   math to make it.
- Compare results with the other   team
Day 3:
Communicate the results
- Each team will make a neat copy of   the scaled drawing
- Do story problems on measurement   from the GED practice book.

As she looked over the plan, she checked to see if it embodied the EFF teaching principles. The lesson was purposeful since it met a real purpose. Hopefully, involving learners in the planning had made what was to be learned transparent. Although some of the practice activities were done in the classroom, the activities were contextualized to a real world experience. The activities also drew on constructivist principles - she had helped students access their prior knowledge of the skill of measurement and they would have an opportunity to build on that knowledge to construct a new understanding of the meaning of measurement and how it can be used in daily life.

Over the next few class periods, the group carried out their learning plan. Although at first Renee had worried that she they had spent too much time on the planning process she found that, having made the plan themselves, students were much more engaged in the process. Of course, not everything went according to plan. Renee hadn’t realized how many sub-skills were involved in making a scaled drawing. After Day 1 she had to go home and figure out how to break down this task and add more practice time..

Renee found that teaching to the EFF standard helped her class stay on track. Since they knew what they were to learn ahead of time, students were more mindful of their own learning processes. Documenting their own learning processes helped them to see for themselves that they were making progress.

After the activity was finished, they used the EFF Role Maps to reflect on what they had learned and how it might transfer to other situations. One student mentioned she could use what she had learning to help her kids with their math problems. Another described how she had seen scaled drawings used as part of the home buying process. A third talked about how he might apply these skills in his work as a mechanic.

When the activity was completed, Renee met with each student to review their work and discuss what else they might need to learn about math and measurement in order to meet their goal of passing the GED. The class also brainstormed other activities they might work on next. The activity had given several students ideas for projects that they might do at home, but they wanted help in planning ahead to see how much the projects might cost. They decided to work on using math to create budgets for projects at home and at work.