Today I want to help students better understand the term value. MP6 refers to attending to precision and in this case, I want students to have a precise understanding of a word that is frequently used in mathematics. I write the word VALUE on the board. I ask if anyone knows what it means? We brainstorm a list of possible meanings. I record them for students to see. We talk about the different meanings and settle on which one (or ones) refers to math. I ask students to record the word and its meaning in their math journals. I want students to understand that value refers to what something is worth, or how much an amount is worth.
I know that we have not helped yet to understand how it applies to math, but we have agreed on a definition that allows us to all be talking about the same thing.
Now I invite students to the rug to explain a new game that they will play.
I begin today by inviting the students to learn a new game. I tell them that I will explain the game and demonstrate it before they play. I show students that today we will only use the cards 2, 4, 6, 8, and 0. We will remove all other cards from the deck. We will play the game in groups of 3. Each group will have a game board, the 5 cards, and 3 colored chips. When it is a player's turn. He/she will arrange the cards in any order and lay them in the center of the board and read the number.
Next he turns over a playing card (different from the number cards) value cards.pdf. It tells the student how many squares he/she may move based on the value on one of his/her numbers. (see the card resource). An example might be if the value of your digit 4 is 4,000 you may move 4 spaces. If the value of your 4 is 400 you may move 2 spaces. If the value of your 4 is 40 you may move 1 space. If the value of your 4 is not here, stay where you are.
I ask a student to be my partner and we each take 2 turns playing the game together. I pick up the cards, arrange them into 42,068 and read my number. I draw my card and it says if the 2 is in the thousands place I may move 2 spaces. My 2 is there so I move 2 spaces. Now my partner repeats the process. I check for understanding and then partner students up and provide them with the materials they will need for the game.
During the game I circulate around to check for understanding of the idea of the value of a number.
If I find students who are struggling, I help them to write out a 5 digit number in expanded form. They can then refer to this as they think about what they have built.
After playing the game, I ask students to return to their desks. I place a deck of cards with numbers from 0 to 9 on each set of desks. I ask each student to draw 4 or 5 cards, create a number as they had in the game, write the number on their paper and then express it in expanded form. I tell students that they will have time to write 4 different 4 or 5 digit numbers on their paper.
Some students will take a number such as 1,357 and write 1000 + 300 + 50 + 7. Others will write the number at the top of an open triangle 1,357 and then at the bottom of the sides of the triangle and adding lines as needed from the top down to a number, write the expanded form at the bottom. The numbers across the bottom add up to the number at the top. I often refer to these as number mountainsnumber mountain.pdf.
I invite a student to come up and show us how they would draw the cards, write the number and record it in expanded form. I check for understanding and then let students work on their own. I circulate around the room to help students who may be struggling, and to informally assess understanding.