Equality & Inequality

Decimal Squares Workshop – Equality & Inequality

Equality and Inequality

 

Materials: Deck of Decimal Squares per group, Decimal Squares Bingo mat per player and markers

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Equality
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Show a transparency of the red square for .7 and ask for descriptions of the green square and the yellow square with the same shaded amount. Demonstrate at the overhead how the transparent squares can be placed on top of each other to illustrate equality.
Show a transparency of the green square for .45 and ask if there is a red square or a yellow square with the same shaded amount.

Ask which yellow squares have equivalent red squares and which have equivalent green squares. Ask each person to select two squares with the same shaded amount and write a verbal description of the equality without using decimals. Ask a few to read their descriptions. For example, the green square with 45 shaded parts out of 100 has the same amount of shading (is equal to) the yellow square with 450 shaded parts out of 1000.

45 parts out of 100 is equal to 450 parts out of 1000

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DECIMAL SQUARES BINGO (Use a transparent Bingo mat to illustrate the game at the overhead.)
Each Decimal Squares Bingo mat should be placed with the colored side face up. This game can be played in small groups but it is a good game to play with the whole group. Place an arbitrary red or green transparent square on the overhead and tell the players to place a marker on their mat if they have a matching square. Illustrate this by placing a marker on your transparent mat, if you have a match. Usually someone will ask if they can place a marker on a square with the same shaded amount, and you can ask the players if they want to allow this “equality version” of the game, which is called DECIMAL SQUARES BINGO MATCH UP. Continue placing transparent squares on the overhead until someone wins the game. At this point, someone may ask if they can continue playing until someone has all 9 squares covered (blackout). The two versions of this game are on pages 72 and 75 of the Decimal Squares Teacher’s Guide.
When the game is over, ask each person to compare the back of their mat to the front. They will see that the decimals are for the squares on the front side. Other versions of this game which connect the model to decimal symbolism involve: selecting Decimal Squares and putting markers on the decimal side of the mat; or selecting Decimal Playing Cards and placing markers on the Decimal Squares side of the mat. This mat can be used for a student activity with one student looking at the decimal side and describing the square corresponding to each decimal while the other student looks at the squares on the other side of the mat to check the responses.
The students in this photo are finding squares with equal shaded amounts and writing descriptions of their two squares.
Photo courtesy of Herb Moyer
Inequality
Write the following question on the overhead: Which has the greater shaded amount, a square with 6 shaded parts out of 10 or a square with 35 shaded parts out of 100? Ask for explanations. One line of reasoning is that the square with 6 shaded parts out of 10 has 6 full columns shaded but the other square has between 3 and 4 full columns shaded. Discuss the important concept here that sometimes 6 of something can be more than 35 of something, if the unit for 6 is larger than the unit for 35. Ask each person to select two squares of different color and write a verbal description of the equality or inequality of the shaded amounts without using decimals. Have a few read their descriptions. For example, 250 parts out of 1000 is less than 40 parts out of 100.
250 parts out of 1000 is less than 40 parts out of 100.
HIGH-LOW Game (see below) This game is also on page 71 of the Decimal Squares Teacher’s Guide. Explain the rules and illustrate the game by selecting an arbitrary square and selecting one player to guess the shaded amount. For each guess tell the player if he/she is too high or too low. After this example, ask the players to turn their squares face down and to play the game in pairs. When the game is finished, discuss strategies and the importance of knowing what type of squares are in the deck.
These students are playing a game called Strategy. This game involves strategy on the part of the players in selecting the squares that they will use for their Hand, as well as strategy in selecting the square to be played on each turn.
Photo courtesy of Herb Moyer

 

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