Mathematics 9 Rational Numbers
Specific Curriculum Outcomes
N03 Students will be expected to demonstrate an understanding of rational numbers by comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers.
N04 Students will be expected to explain and apply the order of operations, including exponents, with and without technology.
N03 Students will be expected to demonstrate an understanding of rational numbers by comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers.
N04 Students will be expected to explain and apply the order of operations, including exponents, with and without technology.
activities
 Two Fractions from Michael Fenton  Place four different digits (from 29) and one operation (+, –, •, or ÷) to create an expression with two fractions with the greatest possible value. This open middle lesson contains a number of excellent extensions.
 Clothesline Math from The Maths Project Journal and Clothesline from Andrew Stadel  One of the greatest tools for teaching number sense is the number line. The clothesline is a dynamic manipulatible number line that makes the facilitation of class discourse on number sense efficient and effective. “Benchmark” numbers may be adjusted when needed, as well as the values that are placed on the line. These two websites give some great ideas on how you could use this to order rational numbers and record student work. The curriculum guide has a similar clothesline idea (p 48),
 Placing Fractions on a Number Line  Joe Schwartz uses an Open Middle Problem to get students to think about comparing rational numbers. The problem is, "Using the whole numbers 09 (one time each) as numerators and denominators, create 5 fractions and correctly place them all on a number line."

 Order of Operations from Open Middle  Directions: Make the largest (or smallest) expression by using the whole numbers 09 in the boxes below. You can change around the spaces and brackets to include fractions or other numbers.
 24 Game  24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by having 4 cards thrown and the first player that can achieve the number 24 exactly using only allowed operations (such as addition, subtraction, multiplication, division, and parentheses) wins the hand. For short games of 24, once a hand is won, the cards go to the player that won. If everyone gives up, the cards are shuffled back into the deck. The game ends when the deck is exhausted, and the player with the most cards wins.
 Using Operations and Parentheses from Illustrative Mathematics  This task asks what numbers you can make with 1, 2, 3, and 4 using the operations of addition, subtraction, and multiplication. After this, you could ask what numbers you can make with 1, 1/2, 1/3, and 1/4. What is the greatest number you can make and what is the smallest number you can make. On page 140 of the MMS9 textbook, problem #7 asks students to evaluate the same expression 4 times with different parentheses. Instead, give the students the expression with no parentheses and ask them to make as many different values as they can just by changing the parentheses. What is the greatest and lowest value? What is the value closest to 0? Place all these values on a number line. I wrote a more detailed description of this activity on my blog.