What's the Difference?

Explicit Instruction/Teacher modeling

• Tell students that subtraction means to find the difference between two numbers. The difference is the amount in which the two numbers are not the same.
• Tell students the story problem, "Kecia and Noah love to read! Yesterday, Kecia read 4 books and Noah read 9 books. How many more books did Noah read than Kecia?"
• Think aloud as you model solving the problem. Ask students to show you on their fingers how many books Kecia read (four). Draw four rectangles on the board to represent the books. Say, "I see the word more in the story problem, so I need to add 4 + 9."
• Allow students think time and an opportunity to correct you. Reflect, "Now I see that I need to solve for how many more books Noah read than Kecia, not how many books they read in all. To do this, I need to compare the two numbers."
• Ask students to show you on their fingers how many books Noah read (nine). Draw nine rectangles on the board directly below the four rectangles, lining them up exactly so the extra rectangles are clear.
• Ask, "Who read more books, Kecia or Noah?" (Noah.) Say, "This drawing helps me to see how many more books Noah read than Kecia." Circle the five extra rectangles.
• Ask if anyone can think of a way to show the difference between the number of books that Kecia and Noah read using a number sentence. Agree that the problem could be solved using subtraction, and write the equation 9 - 4 = 5.
• Tell students to repeat after you, "Noah read five more books than Kecia."
• Explain that less is the opposite of more. Tell students to repeat after you, "Kecia read five less books than Noah."

Guided Practice

• Tell students that today they will play a game called "What's the Difference?" Explain that the phrase is sometimes used to mean that something does not matter, or is not important. In math, the difference refers to the amount to which two numbers differ.
• Distribute twenty counters or other math counting manipulatives to each partnership. Decide who is Partner A and who is Partner B. Ask students what shape the counters are. (Circles.)
• Model the steps to play the game as you write the steps on the board:
  1. Partner A chooses a card and builds the number. (Students follow along as you display a card and show that many counters, for example six.)
  2. Partner B chooses a card and builds the number, lining up the counters below Partner A's counters. (Display a second card, for example four, and show students how to line up exactly that many counters below.)
  3. The partner who chose the greater number says, "____ minus ____ equals __." (Say "Six minus four equals two," and instruct students to repeat after you.)
  4. The player who chose the greater number takes the number of counters equal to the difference between the two numbers. (Point to the two extra counters. Think aloud, "The difference between the two numbers was two. Player A takes two counters because Player A chose the greater number, six." Model moving two counters to the side, and putting the rest back in the middle.)
• Play a few rounds as a class. Display two playing cards, one for Partner A and one for Partner B. Check that students accurately line up the counters to solve for the difference.
• Require that the students say a number sentence before they take the counters. Check that students understand that the player with the greater number takes an amount of counters equal to the difference between the two numbers, not the total number of counters.
• Tell students to describe the steps to play the game to a partner using the transitional words first, next, then, and last.

Group work time

• Distribute playing cards to partnerships. Walk the students through one round with each partner choosing a card.
• Circulate and assess that students are able to accurately compare the numbers to find the difference.
• Listen that students are able to say a number sentence that shows the difference between the two numbers.