## Friday, April 26, 2013

### May Calendar Board

Is that daily calendar routine becoming "too routine"?  Here is an idea to use in May to practice creating addition and subtraction stories.

This is the completed pattern that you will use for the month using the + and - symbols, which is an AABBBB pattern.

Each student needs a  Whole-Part-Part laminated diagram,  and a  dry erase marker.

The teacher presents the numbers to use on the chart. For example, "Today I have 10 in all.  (Hold up a set of ten linking cubes.)  One part of my ten is  8 (There are 8 green connecting cubes). The other part of my ten is 2 (There are 2 yellow connecting cubes). As the information is given, the students are filling in  their diagram.

"Now, let's look at our calendar. Predict whether the math symbol for today will be a plus sign or a minus sign."
"Yes, today is a plus sign. So we will be creating an addition story using our numbers on our Whole, Part, Part diagram. I'm going to give you 2 quiet minutes to write your addition equation, and think about your addition story.  No talking as this is quiet thinking time."

"Now, let's TURN AND TALK to our partner and share the addition story that you have been thinking about. Later, I am going to ask 2 student to share their story with the whole group.  Please share your story now with your partner."

Student One: " There were 8 girls playing at my house. 2 boys came over to play too. Now  there are 10  kids playing at my  house."

Student Two:  "I  have 2 pieces of gum, and 8 chocolate kisses. I have 10 pieces of candy to eat."

The  teacher writes the equations on her diagram as the students are sharing their stories.

Deborah

## Thursday, April 18, 2013

### 8 Times Tables Pattern

When I look at the multiplication tables, I see patterns. Let's take a look at the  8 Times Tables.

.

 8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80 8 x 11 = 88 8 x 12 = 96

First look at the first five facts. Do you see a pattern?
 8 x 1 = 08 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40
If I look at the ten's digit that number is one less than the number multiplied by eight.
• Eight times 1 starts with 0
• Eight times 2 starts with 1
• Eight times 3 starts with 2
• Eight times 4 starts with 3
• Eight times 5 starts with 4
Now look at the next 5 facts. Do you see a pattern?
 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80
Eight times the number starts with two less than the number
• Eight times 6 starts with 4
• Eight times 7 starts with 5
• Eight times 8 starts with 6
• Eight times 9 starts with 7
• Eight times 10 starts with 8

Now look at the next 5 facts. Do you see a pattern?

8 x 11 = 88
8 x 12 = 96
8 x 13 = 104
8 x 14 = 112
8 x 15 = 120

Eight times the number starts with three less than the number
• Eight times 11 starts with 8
• Eight times 12 starts with 9
• Eight times 13 starts with 10
• Eight times 14 starts with 11
• Eight times 15 starts with 12

Note that within each set of five facts, the ones digit follows a pattern :
8, 6, 4, 2, 0

This brings us the question....Does it keep repeating?  I'll let you figure that out yourself. I wouldn't want to spoil the surprise.

Deborah

## Wednesday, April 17, 2013

### Measures of Center Applet for 6th Grade Classrooms

I discovered  a great resource that visually helps to understand the 6th Grade Common Core Standards that develops understanding of statistical variability. The resource is a JAVA application called "Measures of Center" from www.maine.edc.org The site looks like a sign-in site, but the applets/technology tool lists for student and classroom use are located at the bottom of the page and no login is required.

"Measures of Center" lets you explore mean, median, and mode through the use of an interactive line plot. Modify the line plot by dragging on Xs representing data. The measures of center are shown graphically and the values are computed dynamically as data is added to the graph. The maximum data can be adjusted to accommodate a wide array of values. One to ten data points can be displayed at a time.

I like that  you can add pieces of data to the line plot and SEE the results of that additional data reflected in the median, mode, and mean immediately.

This applet will allow you and your students to see the results of how the measures change based on the data.  What would be the effect of an outlier data point? What can I expect to be the effect on the measures of center when the data has a small spread?  What can I expect when the data has a larger spread or range?

I think students need exposure to these types of questions so they can develop a sense of what to expect.  How can they ask themselves if their answers make sense, if they can't predict an effect that is normal?

Explore these questions one day, and then the next day create a line plot and have student PREDICT what to expect if you add an outlier, have a small range of data points, have a large range of data points. Make them start to predict... and think about math not just calculate the mean, mode. or median.

I just bought  a Jenn-aire refrigerator that had to be ordered and I waited for a period of 51 days for that appliance.  I think Jenn-aire should look at the mean number of days that their customers wait for appliances that are ordered from their company.  Is the spread of "number of days" that their customers wait for their products large or small? Are there outliers, and are those outliers satisfied with their customer service or be repeat customers in the future?  Remember that mathematical questions are asked about everyday life situations because MATH MAKES SENSE OUT OF THE WORLD.

Deborah