This video was taken in my class two weeks ago by a friend. The video shows two students playing a math “game” while independently practicing two digit addition. Using two dice (or die, I could never tell), one student rolls the “tens” while another student rolls the “ones”. They do this twice, writing down the two digit addition problem they have created. Then, they add using manipulatives. Listen carefully to the boy’s think-aloud. He actually says he “expands” the number using manipulatives. Then, the two students add using “Spiderman” math. Spiderman math is just a fun way of calling addition using expanded form.
Spiderman math is the scaffolding step between using manipulatives and the standard algorithm. These two students are not quite ready for the standard algorithm yet, but they are more than proficient with manipulatives…they are in the in-between stage, thus they use both manipulatives and Spiderman math.
These students are not ready to regroup, which is the old fashion carry and borrow concept. The next problem they do which involves regrouping, they become totally confused. They are able to do the problem using manipulatives, but don’t know what to do even in Spiderman math. Imagine forcing these students to use the standard algorithm immediately. They will spend the next two to three years of their lives randomly putting a “1” on top of their addition problems. Ask third and fourth grade teachers if this is not true. Allowing them to first explore addition using manipulatives, then Spiderman before the standard algorithm will help them understand when and why regrouping is necessary.
Other students in the class are at various stages. Six students can only use manipulatives, and even then, two or three are having difficulty counting. Two students are able to add two and three digit numbers using mental math quickly and accurately because they can visualize expanding the numbers, mentally grouping the tens and ones together. And yes, I teach them this because if they can do this, they are truly understanding addition. They are definitely NOT adding one column of number, then moving to the next to add that column of number, which is what many teachers demonstrate to students, thinking that the shortcut will help the students get the right sum. Yes, the shortcut will get the students to the correct sum, but it will not help them understand addition and learning how to regroup will become even more difficult. How do I know that these two students are not simply adding one column, then the next? I listen to their think alouds.
Our class have not started learning to regroup yet, though most of my students are already able to do it using manipulatives.
I like teaching math like this. I use games rather than an impersonally generated sheet of problems because the students are more motivated and they have fun. Given a choice between a sheet of problems and generating your own problems using dice, which would you have more fun with? Here, I am also tapping into many different modalities. My tactile students have the dice and manipulatives. My social students have partners. Obviously, my verbal student is talking himself through his problems. My visual students can see the numbers using manipulatives. What other modalities can I tap into?
For the past 7 weeks, I have used this modified triangle as a graphics organizer, originally developed by Andrew, to teach my second grade students math fact families. Fact family is part of our daily math activities. For about five minutes every day, we look at one new fact family and explore relationships between the members of the fact family. Here’s a picture of the latest fact family that we are working on.
As you can see, it’s just a laminated piece of paper that I reuse every day.
Our math assessment, which we took just last week, showed me how incredibly successful using the triangle is in teaching fact family and many relationships that are embedded in fact family. I’ll give you the hard numbers when the scores come back from the district, but a teacher look-see showed me that almost all of the students got all of the related fact family questions correct.
My students and I do what we call “Daily Math”. We break up our one hour of math time into two parts. We spend 20 minutes a day on daily math and 40 minutes on a new lesson. Currently, daily math contains counting time, which I will blog about later, “Today’s Fact Family”, patterns, and one word problem. We do daily math as a whole group on the carpet. Daily math is where I build number sense and practice key concepts.
For the last two weeks, my students have been having fun learning math in non-textbook ways. One game that we have been using on a daily basis for about five minutes each day is “Finger Math”. It quickly gives students practice adding and subtracting in a fun atmosphere, with manipulative support. This activity is easily differentiated and appropriate for first graders, second graders, third, fourth, and so on!
- Have two students face each other.
- Each student choose a number from 1-10.
- When students are ready, they show their number using their fingers.
- Have students quickly add all fingers shown from both students and say the answer.
- The student with the correct answer wins a point. Have students check by counting all fingers.
- Play continues until one student wins. In my class, that’s five points to win.
- Subtract the student with the least fingers from the student with the most finger.
- Play with one hand instead of two hands (meaning 1-5 instead of 1-10) for students who aren’t ready to add the higher numbers. Differentiated instruction.
- For more difficult problems, have three or four students play against each other. This is also an excellent scaffold for adding three addends.
- After each play, have students write the corresponding number sentence in their math journal.
- Instead of adding or subtracting, have students multiply.
Originally uploaded by cityteacher
For math tomorrow, we’re going to use real m&ms to sort, tally, and graph. Lots of valuable math skills involved. We’re also using many different modalities and two graphic organizers. Math should be like this every day! The kids love this every year! I usually do this with the third graders, but with a little modification, you can do the same with younger students and older students.
Make sure you bring enough m&m bags for everyone. I will have the students work in pairs, but everyone should have their own bag of m&m to eat.
There are two pages to this activity. The first page is the sorting, tallying, and graphing sheet. The second page has the questions that students must answer using their graphic organizers.
Here is an illustration of how to use triangles to teach addition and subtraction math facts. See also that the commutative property of addition is embedded in the triangle. Also, notice that the significant number is at the top of the triangle. That is a visual reminder to students that subtraction is anticommutative, rather than commutative.
Thank you Andrew for introducing me to this idea! Next, adaptation for the kinesthetic learners!
I learned this strategy from Andrew. Using triangles to teach math facts may become my favorite method for teaching math facts because it is small visual guide jam packed with a lot of facts! Memorizing is always difficult for my students and a visual like a triangle would be a great mnemonic for them.
Instead of multiplication/division, you can also teach addition and subtraction facts.
I’m thinking that, once students are taught how to use these triangles, they can have triangle flash cards to practice with at home and at school.
These triangles don’t just teach the facts, though. They are really powerful in illustrating to the students the commutative property of addition and multiplication, thus students understand why math facts work and why you can’t just throw in any number into the mix.
This year, I came up with a pretty interesting way of teaching the classification of triangles.
This is an example of how I prefer to teach math in my classroom, not that I do it all the time. Though I should. Guilty!
1. First I give the students input on the classification of the triangles using a charted graphic organizer.
2. Then, I break the students into groups of threes according to sizes and have have them make triangles using their bodies and identify the triangles. This activity goes on for about 7-10 minutes. The kids have lots of fun!
3. While they are doing that, I’m taking pictures.
4. We conclude the lesson by reviewing the types of triangles we learned, what are their features, etc.
5. We have guided practice and independent practice in the math workbook.
6. I go home and make this worksheet using the pictures I took. (Well, a similar worksheet as I lost a few things during the transfer to my new computer). A digital camera, a printer, and a computer equipped with Publisher is just wonderful!
7. The next day, they get this for homework as reinforcement along with their regular homework worksheet from the book.
A lesson like this touches on many modalities. The visual learners have the graphic organizers, the kinesthetic learners use their bodies, the social learners are working with their friends, and so on. The lesson is fun and engaging, yet purposeful. The lesson also builds relationships and connections. Children who take home my teacher created worksheet with pictures of themselves and their classmates remember the lesson better than the children who only take home the impersonal commercial worksheet.
Apology: The worksheet you see above is a redux of the original. I lost the original during my move from old to new computer. I also lost the really great pictures that I used in the original, so these pictures don’t clearly show which triangle is isosceles, which triangle is equilateral, etc. But, it gives you an idea of what we did.