Hamilton-Wentworth DSB Lesson Study #2

Detwiler Towers

by Virginia Hewick, OCT (facilitator), Susan Lenarduzzi, OCT, Alyson Gibson, OCT, Christopher Sackfie, OCT, Sarah Sanderson, OCT

The Problem-Solving Context

Lesson Focus

Arrays as a model for multiplication

Curriculum Expectations

Relate the multiplication of one-digit numbers and division by one-digit divisors to real-life situations, using a variety of tools and strategies (place objects in equal groups, use arrays, write repeated addition or subtraction sentences).

Problem Description

The focus of this lesson is the distributive property of multiplication. Students will decompose the whole into groups by creating smaller groups (arrays).

Actual Problem

It’s midnight at the Detwiler Towers apartment building. People are wasting electricity because some of the lights have been left on. How many lights have been left on at Detwiler Towers? How do you know?

Use pictures, numbers and words to explain your thinking.

Materials

Chart paper and markers
Counters, linking cubes
100s charts
Picture of apartment building (see Appendix A)

The Problem

Getting Started

Use pictures of fruit organized in crates (apples, lemons, plums). Ask students:
- How many fruits are in this picture? How do you know?
- What do you notice about how the fruit is organized? (Possible answers: arranged in rows, columns, two crates allow for doubling)
Bring out strategies such as skip counting (by 2s, 3s, 4s, 5s) and doubling.
Model student thinking beside each picture using math symbols and tools (number, line, picture, etc.).

Working on It

Students will work in groups of two to complete the problem.

See Appendix A for the enlarged picture of the apartment building, showing darkened windows as lights turned off and white windows as lights left on. Students were asked to show their solution in two different ways.

Anticipated Student Responses

Repeated Addition:

6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 48

Multiplication:

6 x 9 – 6 = 48

Skip counting:

6, 12, 18, 24, 30, 36, 42, 48

Arrays:

7 x 6 = 42 (7 rows with 6 in each row)
2 x 3 = 6 (2 rows with 3 in each row)

7 x 6 = 42

2 x 3 = 6

42 + 6 = 48

Reflecting and Connecting

Student work was grouped to create a bansho based on the strategy used. Connections were made between the solutions to highlight similarities between and within the strategies. Reflection questions included: