Mathematic Games with Grade 5's

Analysis of the Problem

The key mathematical concept involved in the first school visit was multiplication. The students will participate in different activities to analyze and solve various multiplication problems. From our experiences with children of any age group, we think that students will have varying multiplication skills and abilities. Particularly, we think that it may be difficult to conduct a group-entered activity that will allow all students to participate equally and feel confident. Additionally, a 45-minute time slot is quite short for introductions of everyone and does not allow for a thorough lesson and activity.

Your Preparation

Our group created two different activities based on multiplication. First, we restructured the game “headbands”, which involves a small card with a product on it placed on the forehead of one student. The rest of the group must come up with a multiplication equation that equals the number on the card and the student must guess the number based on their peers equations. Second, we took the card game “war” and took all of the lettered cards out leaving only numbered cards in the deck. The deck is then split up between a pair of students and each student flips one card over to display the number. The students must multiply the two card numbers together, the first to find the product gets to keep that pair of cards. The goal is to collect as many cards as possible.

For our first game, we chose products of multiplication equations from 1 to 12. We brought scrap paper and pencils, as well as a multiplication chart for students to check their thinking. We anticipate that children may use the paper and pencil to draw groupings or break down equations into simpler forms to multiply or add. For our second game, we made two different decks of cards; one deck contains all the numbered cards from 2 to 10; the other deck contains cards from 2 to 6 for those students who are less confident with multiplication. We will also provide the students with a multiplication chart to check their answers if one of us is not immediately available. We were slightly worried we would be unable to answer all their multiplication questions. We were also worried that the students would be unengaged if they did not enjoy mathematics, however, we hoped they would like these games.

The Visit

When we first arrived and got into our group, we introduced ourselves and asked the students to do the same. They were excited to be working with us and were eager to begin our activities. Before we began, we asked our group how they felt about multiplication and how high they could multiply. Most of the students were not fond of multiplication, except for two students. They told us that they had been practicing their multiplication times tables from 1 to 20.

At random we chose numbers for each student from the pile and they held it to their foreheads. The first round was very slow and challenging for our group. Every student except one struggled to both construct equations and solve them. We went around the table and sat with the kids to facilitate strategies to solve the problems. Some strategies we used were drawing groupings (e.g. 4x6; four groups of 6 sticks) and counting the total; finding familiar or easier equations (e.g. 6x7; 6x6 is 36 so 36+6=42); and creating addition equations (e.g. 7x4; 7+7=14, so 14+14=28). The group found it hard to work backwards and create an equation for their classmates to solve. We gave them a few minutes to think; however, if they couldn’t think of one we would give them one number to work with (e.g. if the number is 56; “7 multiplied by __?”). After the first round of headbands we were able to gage the group’s multiplication abilities so we specifically chose lower and easier numbers to give the students to increase their self-esteem. The second round was much more successful and the students were quickly able to come up with an equation. We continued to give prompts when the students struggled but they were mostly able to orchestrate the activity on their own, which demonstrated increased confidence and motivation to participate. Unfortunately, we did not have time to complete our second activity.

Anticipation

We anticipated that the students would be able to multiply up to their 12 times table with mental math. Another way they could multiply is by creating multiple groups and counting the total. We anticipated they would have memorized some of the multiples to aid them in finding the solution. However, we overestimated the students’ multiplication abilities. When we heard they were practicing their multiplication tables from 1 to 20, were worried that our activity was going to be too easy and not occupy the entire 45 minutes; however, we found precisely the opposite.

Monitoring

Our students were pretty well-behaved; they were quite interested in us and had lots of questions (unrelated to math or learning), but mostly remained on task throughout the activity. We had one girl in our group who joined a little late and missed the introductions. When it came to her turn another student ruined the game for her, so she hardly talked, put her card down and did not want to participate. We think introductions are important and that she could have excluded or lost since she missed the instructions. We did not have the chance to talk to her or encourage her because she left the group. Moreover, math could be a challenging subject for her or she could have been shy and did not feel comfortable to participate. We noticed when the students had trouble solving the problem, most immediately wrote the exact equation on the paper and paused before proceeding. Afterwards, most students created groups of tallies’ and counted each individual tick.

Selecting

Since this game was continuous and did not necessarily have an end goal, the students did not have to present their work. However, at the end, we discussed a few strategies we noticed were occurring. One student who had a greater sense of numbers and was able to use some mental math along with addition. We selected another student who drew out all the groups. As well as one student who rounded the multiples to an easier number and used subtraction.

Sequencing

We came together as a group to decide what fun activities we could do with the students at the school visit. We knew we wanted to do a game-based activity since we figured most of the time students are sitting at their desk doing written work. We headed down to the resource room and took a look at what materials we could rent out to incorporate in our activity. We came up with a game that everyone could be involved in and that incorporated multimodal learning. We decided to play two games with the students that would challenge them and work on their multiplication skills. Prior to picking the game we did not think of sequencing or the breakdown of our lesson. We decided to play the headband game “Guess that Multiplication” with the students first. We planned to play the "War Game" second, but ran out of time, in the future we would need to work on our time management

Connecting

At the end, we compared multiple solutions and asked the students to tell us which they thought would be more effective. Many of the students agreed that counting each individual tally mark would be much slower than starting from a previous math fact and adding to it (eg. 5x6; 5x5=25; 25 + 5 = 30). One student reminded the others that multiplication is a quicker way of addition. Finally, another student shared with the group how she likes to solve multiples of nine with her fingers. Realizing after gathering this information that most of the students are visual learners. Therefore, being more prepared to accommodate all learners out there.

Next Steps

We learned that every student learns differently and works at their own pace. We learned that number sense is quite important for students in order to manipulate the questions to make it simpler. On our next opportunity we would start off with an easier version of the game. We could ask a few sample questions in order to determine what level our students are working with. Do a quick review of the multiplication, looking at the multiplication chart and go over little tips on how to get the answer. On our next visit when we create our math games/lessons we will ensure we have enough time to complete them. We need to keep track of time and organize how long each of the activities we've planned for will be. We will assign ourselves roles of whom will speak, who will demonstrate and who will assist the students in order to not complicate our instructions to the group.