Ancient Egyptian Multiplication

I created this video for the Thinking Math class that I facilitate. To develop an complete understanding of multiplication, one must understand that multiplication is about groups of a specific number. Being able to decompose or recompose numbers is a higher level skill that shows number sense. The Egyptians had this down. This video is helpful for building the idea that multiplication is about equal groups.

Number Line Activity

Here is a short video that you can use to help you further understand how to do a number line activity.

Note: Remember that if you have the same representation of a number (such as the number 1 and the fraction 4/4, these occupy the same space on the number line.

Creating Mathematicians

Standards of Mathematical Practice (SMPs)

If you are not already familiar with the Common Core Standards of Mathematical Practice, you should be! They are 8 principals for that should be used to provide math instruction. They are as follows:

1.       Make sense of problems and persevere in solving them

2.       Reason abstractly and quantitatively

3.       Construct viable arguments and critique the reasoning of others

4.       Model with mathematics

5.       Use appropriate tools strategically

6.       Attend to precision

7.       Look for and make use of structure

8.       Look for and express regularity in repeated reasoning

In other words, we don’t just want our students to be able to do math, we want them to be mathematicians! We don’t spend 6 years teaching students words and definitions, and then start teaching them to read. Neither should we just teach math skills independently and then suddenly expect students to problem solve. Context is just as important in math as it is in reading. That is why one of the ten principles of Thinking Math is “Base instruction on situational story problems” (#3).

Look at the verbs in the SMPs, Make sense, reason, construct, model, use, attend, make use of, express. These are the actions of a mathematician. These are the challenges that face our students.

 So what might this look like in a classroom? Glad you asked. Below is a video taken from a 3rd Grade classroom, but this type of teaching strategy can be applied in every grade.

Site of the Week

Inside Mathematics is a great resource for supplementing Agile Mind. It offers "Problems of the Month" for all grades. Not a "skill and drill" site, but a place where perseverance and precision are required. (CC SMP #'s 1 and 6)

Thinking Through Multiplication and Division

Here is a video from a 3rd grade class regarding the teaching of Multiplication and Division. One of the reasons I would include this on a site for Middle School is that many of our students are weak in in this area. While facts practice is important, so is an understanding of what multiplication and division is. Looking for patterns, developing strategies (such as decomposing), and building their mathematical sense and confidence are elements that are helpful to include when teaching math to any grade.

Standards of Mathematical Practice - Posters

Thanks to Laura Swain for sharing.

Not only is this something that could be posted in the classroom, but little mini-lessons could be built around these principals as well. Both teachers and students need to be aware of these practices and put them into use as we move more and more to Common Core standards.

Click on the example below to link to a PDF of the entire set of posters.

 

 



 

Standards of Mathematical Practice

If you are not already familiar with the Common Core Standards of Mathematical Practice (SMP), you should be. This is what should drive our instruction, as we seek for a deeper understanding of mathematics in our students.

The Math SMP's are very closely related to the Ten Principle of Thinking Math.

Thinking Math began in the spring of 1987! So these principles are not something brand new.

More information will come as we look at each pair of the SMP's in the future.

(PDF's of each sheet are available by clicking on the picture. I highly recommend printing the SMP's and posting them in the classroom.)