Division
Long Division Practice - Making the Remainders "important"
If the kids are having a hard time accepting that remainders ARE in fact important, have them play a game that emphasises the remainders as the part that gets them points! I often had my kids playing a simple board game in order to practice long-division proficiency where the remainder was the most important part, considering the remainder was how many spaces you move if the question is right! I gave each group (of 4) 4 dice, 4 whiteboards, 4 playing pieces, and a gameboard. The first player rolls all 4 dice, and decides how they want them to be arranged (there is often some fairly deeper strategy here if they can do some quick mental math estimation). Then ALL kids playing the game solve for that equation to make sure that the player gets a correct answer. If the player does get the answer right, they get to advance as many places on the gameboard as they had as a remainder!
Division by Halving
Use a template such as the one below to allow students to see how the quotient of a question changes as the divisor changes. By physically manipulating a variable, students can see how the numbers keep halving and halving each time they move down a row.
Use a template such as the one below to allow students to see how the quotient of a question changes as the divisor changes. By physically manipulating a variable, students can see how the numbers keep halving and halving each time they move down a row.
Division Through Interactive Whiteboard
Using the Smartboard is a great way to get kids up and kinaesthetically moving, while also allowing the visual learners to have a connection to the numbers. The picture above is an example of how the whiteboard can be used to introduce the importance of remainders, and how the remainder's significance might change depending on the situation. In this example, the bottom part of this question wasn't revealed until the students had already decided that there is one ticket remaining, and you would just leave it to sell the next night. Once revealing the bottom part of the question however, students can see that the context of the scenario might change the outcome of the question (like being able to sell that last ticket for a different ride instead).
Quotient Cross Out
This game (taken from Boxcars and Oye-Eyed Jacks) is a great and strategic way to get kids to consider the math-facts behind division!
This game (taken from Boxcars and Oye-Eyed Jacks) is a great and strategic way to get kids to consider the math-facts behind division!
Divide My Remainder
Division With Food (Representing remainders as a fraction)
Some of the kids were having a hard time understanding why we would sometimes talk about our remainders as a fraction. The most relatable examples seemed to be ones involving food, and asking students how many __ did we EAT in total. In these examples, we weren't worried about what to do with the leftover pieces, we were simply wanting to see how many WHOLES we had eaten, plus how much (as a fraction) of another whole we had eaten. I brought in Toblerone chocolate and I purposely brought in enough that each kid could have 1/3 of a Toblerone piece, but that we would also have leftovers (but not enough for us to each have one more piece). We had 13 kids, and 6 pieces of chocolate. The kids quickly discovered that we couldn't each get 1/2 of one. We needed to try thirds. So I cut the chocolate up, we divided it out, and realized that although we didn't eat ALL of the chocolate, the amount that we DID use up was 4 whole pieces, and 1/3 of the next piece. We drew a diagram on the board to show how much we ate as well as how much we had left over. We checked our answer with long division, and then used the answer 4 R1 to discuss how the R1 in this example meant that we used 1/3 of the next piece. We weren't interested in the leftover chocolate here, we were asking how many pieces total WE ATE. After this example the kids seemed to have a much better clarity of the division with remainder questions, so this method is one that I would recommend to other teachers as well.
Some of the kids were having a hard time understanding why we would sometimes talk about our remainders as a fraction. The most relatable examples seemed to be ones involving food, and asking students how many __ did we EAT in total. In these examples, we weren't worried about what to do with the leftover pieces, we were simply wanting to see how many WHOLES we had eaten, plus how much (as a fraction) of another whole we had eaten. I brought in Toblerone chocolate and I purposely brought in enough that each kid could have 1/3 of a Toblerone piece, but that we would also have leftovers (but not enough for us to each have one more piece). We had 13 kids, and 6 pieces of chocolate. The kids quickly discovered that we couldn't each get 1/2 of one. We needed to try thirds. So I cut the chocolate up, we divided it out, and realized that although we didn't eat ALL of the chocolate, the amount that we DID use up was 4 whole pieces, and 1/3 of the next piece. We drew a diagram on the board to show how much we ate as well as how much we had left over. We checked our answer with long division, and then used the answer 4 R1 to discuss how the R1 in this example meant that we used 1/3 of the next piece. We weren't interested in the leftover chocolate here, we were asking how many pieces total WE ATE. After this example the kids seemed to have a much better clarity of the division with remainder questions, so this method is one that I would recommend to other teachers as well.
Other good resources worth checking out:
The following games are posts that I had found on Pinterest that look like they could be really great games as well, I just didn't end up getting the chance to explore with them!
The following games are posts that I had found on Pinterest that look like they could be really great games as well, I just didn't end up getting the chance to explore with them!
Remainders Wanted
http://www.teacherspayteachers.com/Product/Remainders-Wanted-Long-Division-Game-164429
Kids take turns rolling a 10-sided die to find their divisor. Then they choose one spot on their card of dividends to cover up with a chip so that they know that they have already used that dividend. They do the long division, and write their remainder as a "score". After 10 rounds, they add up their total scores, and the highest score wins!
http://www.teacherspayteachers.com/Product/Remainders-Wanted-Long-Division-Game-164429
Kids take turns rolling a 10-sided die to find their divisor. Then they choose one spot on their card of dividends to cover up with a chip so that they know that they have already used that dividend. They do the long division, and write their remainder as a "score". After 10 rounds, they add up their total scores, and the highest score wins!
Remainder Golf
http://www.teacherspayteachers.com/Product/Division-Remainder-Golf-A-Game-to-Practice-Dividing-by-a-1-Digit-Divisor-505946
This game sounds like a really great way to get kids excited about division. They move from hole to hole, using the hole number as a divisor for a question as they draw a "golf ball dividend". Their score is kept on a golf card until they can total it up at the end!
http://www.teacherspayteachers.com/Product/Division-Remainder-Golf-A-Game-to-Practice-Dividing-by-a-1-Digit-Divisor-505946
This game sounds like a really great way to get kids excited about division. They move from hole to hole, using the hole number as a divisor for a question as they draw a "golf ball dividend". Their score is kept on a golf card until they can total it up at the end!
Remainder Racoon
http://kidsactivitiesblog.com/11621/make-your-own-math-game-division-remainders
Try to get the racoon from start to finish! Look at the number your marker is on, spin the dial to see what you are dividing by, solve, then move the amount that you had as a remainder.
http://kidsactivitiesblog.com/11621/make-your-own-math-game-division-remainders
Try to get the racoon from start to finish! Look at the number your marker is on, spin the dial to see what you are dividing by, solve, then move the amount that you had as a remainder.