Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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ConnectionsSession 06 Overviewtab atab btab cTab dtab eReference
Part D

Applying Connections
  Introduction | Decorative Boxes | Classroom Practice | Connections in Action | Classroom Checklist | Your Journal


Reflect on each of the following questions about applications of the Connections Standard that you saw in Mr. Levy's class. After you've formulated your own answers, select "Show Answer" to see our response.

Question: How does Mr. Levy introduce this problem to the class? Does he suggest a structure for the students' work?

Show Answer
He gives a motivating opening to the lesson and engages the students in the important question of how to determine the correct amount of stain to purchase. He leaves the project open-ended, possibly in order to allow students to find connections on their own, to apply what they have already learned, to learn to organize their own work, and to communicate with their peers.

Question: What previous knowledge and skills do students need to bring to this task?

Show Answer
They need basic ruler measurement skills, knowledge of how to multiply length times width to find the area of a rectangle, and the ability to use a calculator to multiply. They need to be able to solve problems in which they find the correct amount for one person (or item) and then use that to find the total amount for many people (items). They need strategies for changing units, such as inches to feet or square inches to square feet.

Question: What evidence is there that students extend their mathematical concepts and skills during this lesson?

Show Answer
Students learn to find more complex areas that are the sum of several smaller areas. They multiply by fractions and decimals and see the relative size of their answers. Throughout the activity, they gain practical experience with estimation.

Question: What connections among mathematical ideas do the students make?

Show Answer

Geometry: Connections are made between a three-dimensional figure, its two-dimensional faces, and the areas of each.

Measurement: Students connected measurements on a ruler to fractional numbers of inches and to equivalent decimals on a calculator.

Algebra: Students related their knowledge of the formula for the area of a single rectangle to algebraic expressions for calculating the total sum of the box's surface area. In addition, students were informally prepared for simplifying the problem by combining like pieces, which is related to their future work in algebra, when they will combine like terms in algebraic expressions.

Number: Connections were also made between students' estimation skills and developing number sense.


Question: What connections to the real world do the students make?

Show Answer
Students connected their calculations of the area to making estimates based on paint labels and prices. They carefully considered how real boxes are built (for example, the inside must be a bit smaller, because the edges had to be glued together), and connected that to their calculations and estimates. They also learned how to plan for measurement and calculation errors, and connected that to estimating the materials and the price.

Question: What connections to other Process Standards are evident in the video?

Show Answer
The investigation was tackled as a group problem-solving experience, and many strategies were used. Students also communicated verbally and through recordings of their calculations. They used the pieces of wood as objects and didn't seem to feel a need to draw or label diagrams, but they appeared to use simple number sentences to represent parts of their work. During the whole-class discussion, they verified and sometimes revised their solutions based on consideration of another classmate's reasoning about the problem.

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