Students will start today's lesson with a fluency assessment. This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.
This is an assessment I have my students do each week and then graph their results. It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions. (It also happens to be the quietest time in my math classroom all week!!)
This is what my classroom looks like as students work on this assessment.
Please check out the resources to hear my thoughts about students fluency progress. Since students began the fourth grade set today, I anticipate students graphs to decrease in the number corrected and attempted.
Click here to see an example of a typical fourth grade fluency decrease now that students are completing the fourth grade fluency set that incorporates division, multiplication, addition, subtraction, and adding and subtracting fractions with like denominators.
Note: I do not start my students with the fourth grade skills, however, at this point in time, all students are working on the fourth grade set. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards. By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics. I want to make clear that this assessment ONLY measures basic math computation. It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year. Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.
Students continue playing the Pizza Picasso Game they started in yesterday's lesson. Students were not able to finish the game yesterday, and I also wanted to provide students another chance to practice the skill and procedure of expanded notation as well as provide for an environment in which I could easily circulate around the room in order to observe, question and guide students thinking.
For this lesson, students will play a game called Pizza Picasso in order to practice the expanded notation method for division and review multiplication. Students build their understanding of multiplication and division as inverse operations as they use multiplicationto check their division which allows much practice in CCSS 4.NBT.5 and 4.NBT.6. Students have spent several previous lesson exploring division methods. This lesson is important because it allows students an opportunity to be comfortable with a numeric based division method. As students move away from the place value chart method and pictorial strategies, it imperative that they have an alternative effective division strategy. While the place value method helped build a conceptual understanding for division with my students, it is not always the most efficient method.
I want my students to have an efficient method to divide upon the completion of this division unit. I chose this game because I like that students must use multiplication to check their division which reinforces the relationship between the two operations. I also like that the game uses pizza, a food that many fourth graders love and eat a lot of!
Materials to Play the Game
• Pizza Picasso Coloring Sheet (one per player)PizzaPicassoACommonCoreFastPacedLongDivisionGameforththGrade.pdf
• Scrap Paper
•one set of regular playing cards (student's won't play with 10, Jacks, Queens, or Kings)
The object of the game is to complete division problems and be the first player to completely color in the Pizza Picasso coloring sheet thereby winning the game
How to play the game:
1. This game can be played in pairs or trios. ( my students played in trios because we do a lot of partner work on a regular basis. Working in trios adds a level of engagement simply because it's not the norm in my class, whereas working in partners is more the norm.)
2. Each player receives a Pizza Picasso coloring sheet, crayons, a pencil and a piece of scrap paper. Each pair or trio needs cards Ace through 9. Place the remaining Ace through 9 cards face down in a pile in the middle of the group.This pile will be the divisor pile. (When playing with trios, it is very easy to have students quickly sort the cards by suit, and put the left over suit in the middle of the group as the divisor pile)
3. Each player then places their ace through nine cards in a separate face down pile as their dividend cards.
4. Each student draws a card from the divisor card pile to determine who goes first. The child who draws the highest number goes first. Return the cards to the digit pile and shuffle them before starting play.
5. PLAYER 1 selects four cards from their dividend pile. Using these four digits, they create the number of their choosing (if they draw 4, 3, 6, and 5 for example, they could create 4356, 6543, 5436, etc.) This number becomes the dividend.
6. PLAYER 1 then selects a card from the divisor pile. This number represents the divisor. So, for example, if PLAYER 1 decided to create the number 5364 from the numbers they selected from the digit pile, and then draws a 4 from the divisor pile, the division problem they are solving is 5364 ÷ 4.
7. As they are solving their division problem, PLAYER 2 starts drawing cards to create their problem in the same manner. They will begin solving their problem as PLAYER 1 is solving their work. This game is designed to be a fast paced game, where all students are working quickly and simultaneously. Students can tend to get loud. I remind my students that since they are only drawing cards and solving division problems, there shouldn't be a lot of noise in the classroom.
8. When a player completes a division problem, they call “MATH CHECK!” and their opponents use the inverse operation of multiplication to check their work. This is often where great conversation occurs between students which also allows students to utilize Math Practice Standard 3. If it is decided that their work is accurate, they can determine if they can play one of the digits in their quotient.
9. On the pizza, there are digits. Once the division has been completed and checked, a player can look at the digits in their quotient (in this case, 5364 ÷ 4 = 1341). PLAYER ONE could choose to color in a 1, a 3, or a 4 on their Pizza Picasso board. Any digit in the quotient or the remainder can be played (colored), but ONLY ONE digit can be used per turn. If the quotient or remainder is not on the pizza, the player quickly creates another problem, and play continues.
10. As players complete problems, the cards are shuffled face down into the pile.
11. Ultimately, the first player to completely color in their Pizza Picasso board is the winner of the game.
You can see in this video a student is a beginning to make connections between the standard algorithm and the expanded notation method for long division. She is able to experience the standard algorithm on a computer based program my school uses. She admits that the computer "way" seems more difficult right now, but I believe she will make a great transition to this method eventually.
As a wrap up for this lesson, students turned in their pizza sheets, even if they didn't finish. Then, I led a brief discussion asking students what they liked about this game. As you can see in this video, students liked working with each other, some even reporting that they felt like their partners helped them solve and make better sense of division.
I also gave students homework in order to practice division procedures at home as well. In the following photo you can see a grid of problems. Students have a choice for homework. They may choose all of the "A" problems, which are those that are not circled on the grid and all have four digit dividends. Students could also choose to do all of the "B" problems which are circled in the photo which are problems that have three digit dividends. This is one way I like to differentiate homework and give students a choice in their work. When students feel like they have a choice in their homework, they tend to be more engaged in their learning process and also tend to be honest in which problems they choose to do. For the most part, my students who are not quite comfortable with four digit dividends choose the "B" problems, and the students who are capable of four digit dividends chose the "A" problems.