Up this week – Multiplication Bump!
It’s no secret that students in the 21st century learn differently. In the 1950s, roughly 80% of students were auditory learners and learned simply by hearing about something or reading about it in a book. Today, less than 5% of students are auditory learners. Instead, they’re wired visually – they learn by seeing and doing, which is confirmed by how frequently today’s students access YouTube and TikTok if they want to learn how to do things.
We can take advantage of this trend to help buy back time during your math workshop. Instead of spending class time teaching students how to play a math game, which they may or may not remember tomorrow, let them YouTube it!
On Monday, students can watch the video about the game they need to learn (either on our website or YouTube channel) and then collaborate together about how to play by writing down rules, working through different scenarios, etc. Then, on Tuesday, they can play! Of course, they can always go back and reference the video if they want to, especially for the differentia ted levels of play, but they can do so independently!
Since we talked about addition Bump games last week, which are great for K-2, this week we are going to feature multiplication Bump! If students already have a foundation for Bump from lower elementary grades, this concept of Bump Multiplication will be a breeze as they get into 3rd, 4th, and 5th grade! This game could integrate during your multiplication unit or anytime throughout the school year when students need a review of multiplication facts.
While we start Bump Multiplication games in 3rd grade as kids are starting to learn multiplication in that year, Bump Multiplication are also great for 4th and 5th grade as well. Even if you aren’t actively teaching multiplication facts, you might have students that are struggling with x8 – there’s nothing wrong with pulling out the Speed! x8 game or the Bump x8 game just giving kids more practice.
Objective: Be the first to get rid of your counters!
- 10 clear counters of one color
- 10 clear counters of a different color
- Game board
- Note: Just like in regular Bump, you don’t really need a specific game board. Just draw 10-12 circles on a page and in those circles, skip count by whatever factor you are using for the game. For example, if you’re doing Bump x2, you’ll write 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 in the circles. If you’re using regular six-sided dice for the game (see note below), you could also add 22 and 24 for a total of 12 circles on the game board.
- Note: This game works with either 1 ten-sided die or 2 regular six-sided dice. The benefit of six-sided dice is that they are more commonly accessible, and they give you a greater range of play as you have the option of going up to 12 times a number since you have 12 faces. It’s up to the teacher to decide which tool to use.
In our free game boards, we tried to condense it, so one board would work for either 10 or 12 circles. It has 10 circles that are in a bolded color, so if you did have a 10 sided die, you could use that option, and then we have two additional circles that will be a little less prominent that will be the x11 and x12 values.
Just like Bump Addition, there are three levels to Bump Multiplication so you can differentiate based on your students.
- Roll the die.
- Multiply the number on the die by the factor of the game.
- Place counters, Bump or Crown the product – see variations below for more specifics.
- Continue rolling until one person is out of counters.
Roll the die. Anything you roll will be multiplied by the factor of the Bump game you’re playing and you put your counter on the product.. For example, if you’re playing Bump x4 and you roll at 5, you will times 5 by 4 to get the product of 20 and you’ll put a counter on the 20. If my partner rolls a 6, he multiplies it by 4, and then puts his counter on the 24 as the product.
If I roll a 6, I can “bump” my partner’s counter off the 24 and put mine on it instead. If I rolled a 5, and I already had my counter on 20 I would add a second counter to the 20 and crown it. This would mean that I owned the 20 and I was “unbumpable.” Anytime anyone rolls a 5 for the rest of the game, they’d lose a turn since that number is unavailable.
There isn’t a lot of strategy involved in level 1.
The next level adds a bit more complexity to the game. You’re still working with products, but you’re also helping kids understand how to decompose a product into different parts that add up to the total.
For example, if I rolled a 5 and am playing Bump x4, I could A) put that counter on 20 if it was available for me, or B) put it on two addends that total the product. Remember the board is skip counting by 4s, so I could put one counter on 16 and one on 4 as the sum of those numbers is 20 and I got rid of two counters instead of one.
If my partner rolled a 4, later on, they could put a counter on 16, or put two counters on 8 in order to crown it or bump me off a space I was using.
Level 3 – Unlimited
Bump Unlimited has the most options for getting rid of counters, as does addition during addition Bump – take the product and decompose it into as many addends as possible. The idea here is to get rid of more than 2 counters and he helps your students become a bit more strategic and forward thinking.
For example, if I roll a five, 5 x 4 = 20. I could A) put a counter on 20. B) put a counter on 4 and 5 or 20, or C) put one counter on 12, then two counters on 4 (to crown it!), which total the product of 20.
The strategy comes in here as all the “good numbers” – the easier, smaller numbers – generally get used up first. After those numbers are gone, you really have to get creative to use some of the bigger numbers!
Accountability sheets are vital to the success of your Math with Someone station, especially in the upper grades, while you’re working with students at your Math with Teacher station. You know how it goes – it looks like they’re playing their game, but who knows what they’re really doing!
For Bump games, making an accountability sheet is quick and easy. Students can create their own really quickly. Have them record the first 8-10 facts they get as they play. If I rolled a 5, I would write down the 20 as the product.
Don’t tell the students, but I actually don’t even look at these accountability sheets. Just having the kids turn the accountability sheet in to you helps them know that, while they’re at these stations, they’re accountable for doing the job they’re supposed to do. I use it as a check-in and then toss them later on!
Storage and Logistics
The pieces for Bump are kept on the Math Salad Bar, as usual. If you download our free game board, you need three copies of game board and any other documents in our game binders. You don’t need a game board for every student, so within a game binder, we’d have three copies of each game board in a clear plastic sleeve so you could potentially have 6 students go to that station. If Partner A gets the game boards and materials, maybe Partner B can choose the version of Bump you’ll play!
Bump Multiplication lends itself very well to differentiation. Students could be working on different facts in different groups, but we strongly suggest that you follow our progression for how you actually go about teaching those facts. No longer do we start at x2 and go all the way up past 10. That method promotes memorization of patterns, which might work for x2, x3, x4, and x5. However, once we get into x6, x7, x8, x9, that all falls apart. Instead, we need to teach the concept of multiplication and help students see the patterns rather than memorizing a procedure. Not familiar with our progression of multiplication facts? Check out our free download of this sequence along with our companion product and one of our best sellers, the Making Sense of Multiplication Journals.
Our progression: We always teach the x5 and x10 together, then we do the x2, x4, x8. Next, we teach, x3, x6, x9 together, and then the x7 is taught alone. Make sure you put your Bump! Game boards in the correct order as well! There are several blogs on this topic of the progression of multiplication facts if you need more info!
Multiplication Speed! is another really great companion tool to go along with this game. Speed! And Multiplication Tetris will be featured next week in our blog!
Bump x10 and x100
This option takes Bump to another level. In 4th grade, students are starting to learn how to decompose in multiplication, as well as how to do partial products using an area model. One of the key things that students don’t understand or have a very shallow understanding of is the idea of multiplying by 10 or 100.
We might have been taught a procedure for this operation – if we have 17 x 10, just multiply the 17 times 1 and then add the zeros back. While this might be a great shortcut, how many students (or adults for that matter) really understand what just happened in that situation? What happened to that value? When students get to partial products with the area model and eventually polynomials with X as a value in middle school, they won’t understand what happened. In 5th grade, when they start multiplying or dividing fractions, they’ll also need more than a memorized procedure to be successful.
So, we created Bump x10 and Bump x100 that are both placed well in 4th grade.
The same rules apply in these games as any of the other Bump games.
- 10 clear counters of one color
- 10 clear counters of another color
- 2 regular dice
- Note: we’re going to be using two six-sided dice here because then students can go all the way up to 12 x 100 or x 10.
- Place Value Discs – Optional
- Note: If kids need it, they can take the place value discs out from the Math Salad Bar and actually act out what’s happening with the numbers. If I had 12 and wanted to create it 10 times, I could easily see what’s happening to the place values of the numbers. Place value strips would also work here.
All the rules are the same except that when I roll, the sum of the two dice will be multiplied by 10 or by 100.
Bump x10 Examples:
- Level 1 – I get a 5 and a 6, add to get 11, and then times it by 10. I’d put my counter on 110. My partner might roll 8, multiply by 10, and then put a counter on 80.
- Level 2 – I get an 8 by rolling a 5 and a 3. I can put my counter on 10 times the sum, which would be 80, or I could put my counter on 10 times each individual number on the dice – the 50 and the 30, which add up to 80. My partner rolls a 9 with a 5 and a 4. They can put one counter on the 90, or one counter on 50 and one counter on 40 to total 90.
- Bump Unlimited – I roll an 8, times it by 10 to get 80. I can put my counter on any numbers that I can combine to total that product.
Bump x100 Examples:
- Level 1 – I roll a 5 with a 3 and a 2, I multiply that by 100 and put one counter on the 500.
- Level 2 – I roll a 5 with a 3 and a 2, I could put a counter on the product (500) or the individual numbers x100, which would be 300 and 200.
- Level 3 – I roll a 5 with a 3 and a 2. I might get tricky and put 2 counters on 200, crown it and own it, and then one on 100, which would add up to the total product of 500.
Whether you let your students learn to play on their own or you show a video tutorial to your whole class to target your visual learners, we hope you can buy back some of your time during math workshop with these videos!
Additionally, these videos are a great parent resource! Bump is a simple game – almost everyone has regular dice in a junk drawer somewhere and you can use coins or snacks for counters. Send the game home for kids to play with their parents, and direct them to our YouTube Channel to learn the rules!