After years of seeing students mix up math operations in word problems, I have finally figured out how to help students understand what operation to use in word problems. This little word is causing students much of the confusion–EACH. Haven’t we all taken for granted that students understand what this word means. The word ‘each’ is in nearly every multiplication and division problem, but many students don’t know what it means–every one in the group. If we teach students to read a word problem and replace the word each with its meaning, every one in the group, students somehow have a light bulb experience.
In conjunction with teaching students to understand the word each, also asking them questions about the problem helps facilitate understanding. For example when you ask, “Is this a joining or a separating situation,” students start to make sense of word problems. Students generally understand that words like altogether and in all mean that they are joining groups. The word total may need to be taught as a word that means in all, but total isn’t a difficult term for students to become comfortable with.
To help students further differentiate between multiplication and addition, ask questions like: are we adding the same amount over and over or are we adding two different sized groups? If the answer is adding the same amount over and over, then multiplication is repeated addition of equal sized groups. If students are confusing division and subtraction, ask, “are we subtracting different amounts or are we subtracting the same sized amounts over and over. If the answer is subtracting the same amounts over and over, then teach students that division is repeated subtraction of equal groups.
Last week we held a final championship for students in second through fifth grades for the classes’ highest percentage of correct answers during “Math Wars”. “Math Wars” is our affectionate name for math fact races. Surprisingly the underdogs (second graders) won the final championship while a fifth grade class had been winning all year. So, of course as second graders are, they were so EXCITED that they had won– as was their teacher. Since I didn’t have any funding for anything extra special, I, we’ll say ‘renovated’ an old trophy, which I found gathering dust. I cleaned it up a bit and made a new plaque for it as you can see below. I also handed out a golden abacus to each grade level winner. The golden abacuses were awarded and switched among classes all year after each “Math War”. Pictured below are all of the awards. I hope they give you some ideas.
For the math timed tests I used for math wars, click here.
For an example of how a teacher kept up with her own math races to prepare for math wars, click here.
For more about the math fact races, click here.
To practice math facts, spelling words, or any other quick answer type learning, you can play Squat. To play Squat, two students from two different teams approach the board. The teacher calls out a fact or a spelling word. The two students at the board race to answer the question correctly and then they squat when they think they have the correct answer. If they are correct they earn a point for their team.
When I have played this, I usually split my class into two teams. Different students on the teams take turns to be at the board to earn their team points. Team points can be taken away from students who aren’t waiting quietly or who blurt out an answer when it isn’t their turn. Students love this game and will beg to play it after you have played once. If you have some extra time (heh, heh, who has that?!) during a spot in your day, this is a fun way to reinforce skills or fill time.
I am trying something new this year to help motivate students to learn their math facts. I heard about doing Math Wars from another math coach. Each class will give themselves a name for a team. The team could even be alliterated for more fun. For example, Mr. Bowers Brains or Ms. Elwick’s Elephants. Having the students take ownership in what they name themselves promotes more motivation to work towards the goal of learning their facts.
Classes challenge other classes to beat them on their fact races. Grade levels can challenge other grade levels too. For the first Math War at my school, I have decided to just have classes compete with other classes in the same grade. To determine the winner, I am calculating the total amount of items that are correct and taking a class average. This way all of the students are working towards doing better, and there are no tears or frustrations if all of them are not answered. Students will be answering all of the facts in the race, and I will give them two seconds per problem. If there are 60 problems, then students will have 2 minutes to answer all of their problems For the next war classes may compete outside their grade level; 4th graders may challenge 5th graders, for example. One of the teachers at my school suggested putting up schedules like when football games are played. So working with this suggestion, I have placed posters on the walls to add to the anticipation of triumphing over another team. This has added to student motivation since I hear students saying that “we are gonna beat Ms.____’s class”.
For trophies I tried to think of something that would reflect the idea of math and that I could spray paint gold. After brainstorming with several colleagues, someone suggested an abacus. So now I have the GOLDEN ABACUS (angels singing in the background). The golden abacus will be traveling to the winning classes and will go to follow the next champion. I bought several abacuses so that each winning class could have an abacus for each WAR.
I have come across Amanda Bean’s Amazing Dream by Cindy Neuschwanderin several of Math Solutions lesson books, however today is the first time I have read the book. It wasn’t until last year that the book actually was ordered for our library. The book is about a little girl who counts EVERYTHING. She counts so much that she dreams about counting. Her teacher and her mother encourage her to multiply because it works better for counting large numbers. Towards the end of the book Amanda realizes that multiplying REALLY is better than counting everything. This book would also work well for teachers who are using CGI strategies with counting collections because on each page there are multiple illustrations of objects to count like squares in window panes, food, wheels, legs, sweaters etc. Arrays and things that come in groups can easily be discussed after looking at the pictures. Now I am going to recommend this book to all the teachers who are teaching multiplication.
Another math coach related to me today the story of how a student she taught had named fingers sections as something that comes in groups of threes. She took this concept and helped students use this to develop multiplication strategies to learn their threes multiplication tables. Fours multiplication tables can be learned as well if students include counting the top part of their palm. See the pictures below for more clarification.
Here is my door for this year. I just finished it! It took a lot of work, but it turned out so cute. I took the idea from Greg Tang’s book The Grapes of Math. I recycled the grapes from another project in the past to use on my door. The grapes were made from purple and green construction paper circles that I glued together. I then punched a hole through the top with a hole puncher and put some green pipe cleaners through the top. To make the vine tendrils curly, I wrapped the pipe cleaners around a pencil. I recreated the grape vine with twisted brown bulletin board paper. The grapes were made from purple and green construction paper circles that I glued together. To stimulate math thinking, I added a copy of Greg Tang’s poem so that students will be encouraged to count the number of grapes that are displayed.
I wanted to share these multiplication drill sheets which I acquired from a great math coach at another school. There is a sheet that has multiplication facts 2-10, 2-12 and an addition sheet that has facts 1-9. The facts don’t repeat with the commutative property (turn around facts), and they are the ones I used with the teachers at my school in my former post on June 23rd. I am sharing them with her permission below.
Research shows the best way for students to learn math facts is practicing for about 7 minutes daily. With this in mind, we gave a class of students a teacher made sheet of multiplication facts in which none repeated with the commutative property. So if there was a 2×3 fact on the page, this fact didn’t repeat with a 3×2. We timed the students almost daily beginning with five minutes to complete a page of 66 problems 2′s through 12′s facts. Students would count the number they left blank and that they missed and record this on their page. Then their teacher and students would call out all the answers chorally to check. Next their teacher would record the number students missed on a chart. Every week, after students had felt some success, the time was moved down by 30 seconds until the time was equal to 2 seconds per problem (or 2 minutes and 12 seconds). This method proved to be effective for most students because we encouraged them to get just one more right each time. Below is a picture of the chart which shows students times. Each different colored row is when the time changed which you can see listed at the top of each column. The chart shows a time period of about four weeks. Even if students didn’t make it to the goal of answering each problem within two seconds, they made drastic improvements from their beginning test. Ideally more time would have been spent on practicing, however the end of the year was upon us. I was so proud of these kiddos!