Piper's Readings

Break the Boundaries

Introduction:

• Area has always been a topic that has been tough for students to deal with.
• Many students only have a superficial understanding of area
• past instruction has only focused on formula and not learning the actual concept of area.
• Students need experience with:

1. partitioning a region with a two-dimensional unit of measure
2. iterating a unit to cover the region without space or overlap
3. exploring conversation of area
4. structuring an array

The Professional Learning Team (PLT)

• group of elementary teachers team up to do a lesson study on area
• wanted to improve upon students' understanding from a recent lesson on area
• used the lesson study format to design a study

Previous lesson

• called "Shapes, Halves, and Symmetry"
• used various activities to have student cover shapes with a unit of area
• they covered shapes with unit blocks
• teachers felt students didn't have enough time to communicate or engage in hands-on activities
• teachers want students to communicate and justify their solutions

The New Plan

• Teachers devised a new plan to supplement the previous lesson.
• This time, students would use triangle units to cover shapes and they would count the number of triangles used to obtain the area.
• This allowed students to partition a complex shape into known shapes.
• communication was also key

Implementation

• The lesson involved finding all the ways the students found the area of the shapes
• Students had to explain their solutions
• Teachers found that some students initially struggled with the activity because they would count 2 triangle that formed a block as 1, instead of 2. This was later remedied
• This lesson allowed students to recognize using a common unit when computing area.

Taking it further

• Teachers can offer challenges to more advanced students by either having them find the area of a shape they create, or have them figure out if it's easier to measure with bigger or smaller units.

Learning About Area by Working with Building Plans
Introduction

• Students have an over-reliance on using the area formula
• teachers wanted to see how they could help students see the connection between area and direct measurement.
• Teachers wanted students to 1)use benchmarks to estimate area and (2) calculate area from building sketches.
• The Area Teaching was divided into 3 Lessons.

Lesson 1 (Introduction to Area Measurement)

• Students asked what to use perimeter for, versus area.
• students given a square foot linoleum tile and asked to measure its area using a smaller tile unit.
• Methods and answers were compared.
• Students then took linoleum tiles and were asked to measure area in parts of the school.
• The goal of this section was to teach area that they don't have to "fill in" all the space with their tile, but instead, they create rows and columns and can multiple their numbers.

Lesson 2

• Students went to two nearby neighborhood houses and estimated their area measurements.
• They also had to determine a good benchmark (or unit) to use to measure.

Lesson 3

• Students were given floor plans for real houses and asked to determine the area of the living space in the house.
• This often involved students having to add or subtract odd ends. In other words, they weren't finding the area for simple square houses.
• Students worked on this for one half hour and presented their findings on the overhead

Results

• Many students benefited from this lesson with their understanding of area as determined by pre and post-assessments.
• Many students still struggled with determining area from irregular shapes.
• Other ideas for area units include: emphasizing benchmarks for area, designing building plans, and extension to rational numbers.