1. Grade 7 Video Outcomes
N7.2 Expand and demonstrate understanding of the addition, subtraction, multiplication
and division of decimals to greater numbers of decimal places, and the order of
operations.
Synopsis
Clip N7.2A presents the idea of setting up arrays to represent multiplication and division.
The patio problem listed below is presented as a way of understanding the area model of
multiplication and additionally as a way of explaining links with algebra. Although two
digit by two digit multiplication is introduced earlier than Grade 7 the importance of
understanding the array approach and multiplication of two digit by two digit whole
numbers is critical to the understanding of the array approach when dealing with
multiplication of decimals to greater numbers of places at the grade 7 level. In this video,
Mike suggests providing the grade 7’s with Base 10 hundreds, tens and ones and asking
them to try to construct a patio with 168 blocks that most closely resembles a square.
Looking at the base 10 blocks students can see that a 10 by 10 square would include 100
blocks, an 11 by 11 square would include 121 blocks, etc.
Connections to area, multiplication and algebra are all presented in this video.
Connect the words to the diagram
Make Connections to Area
and use color to reinforce the pattern x2 + 4x + 2x + 8
10 + 2 collect like terms X + 2
12
X 14 x2 + 6x + 8
10 8 X
14
40
+ 20 +
4 100 4
12 168
(x + 2)(x + 4) FOIL
Note: This problem was used in a workshop with GSSD administrators in May of 2008.
For a copy of the many solutions generated by administrator’s click on the following link
https://gssdadmin.wikispaces.com/Workshop2 and download the file called day2.pdf.
Problem
My brother had 168 square tiles, which he wished to use to create a patio deck on his
back lawn. He wanted to create a rectangular shape. What are his choices? Which choice
is closest to the square?
1

2. Clip N7.2B presents an explanation of another relationship within and between the base
10 blocks. The cubic decimetre can be viewed as one, the flat as one tenth, the long as
one hundredth and the cubic centimetre as one thousandth. Rather than demonstrating
addition of decimals to thousandths Mike refers to a demonstration provided in the grade
4 videos showing addition to two decimal places and suggests that this understanding is
critical to understanding addition to greater numbers of decimal places.
Clip N7.2C models the question 1.3 x 1.2 by setting up an array within the algebra tiles
organizer. One and three tenths is set up in one direction and one and two tenths is set up
in the other and the rectangle is then formed showing the answer one and fifty-six
hundredths. (1 flat representing one, 5 longs representing five tenths and 6 cubes
representing six hundredths).
Concrete Manipulatives: Base 10 blocks, Algebra tiles organizer
Virtual Manipulatives
Base 10 Blocks
http://arcytech.org/java/b10blocks/b10blocks.html
2