Tools for Assessment and Instruction:

There are five main tools or activities in the Teachable Moment/ Power of Ten System. These tools are used at all levels and increase in sophistication and difficulty as the student moves through the system.

How Many Ways and What do I Know Activities:

These two activities can be very creative for students by involving them in discussions of their thinking and the connections they make over all the operations (+, -, x, ÷). These activities are performed daily in the early years, weekly in the late primary, and monthly in middle school. Click here for a short video.

Patterns and Relationships and Projects (Problem Solving and Problem Posing):

Younger students who are able to pose problems using numbers often show an increased understanding of the relationships between numbers and proficiency with their basic facts. This activity is never less than twenty percent of the program, and slowly increases to almost forty percent in the middle years. Projects such as designing a house, planning a party, or collecting data about their peers, help students make connections between mathematics and daily life in their homes and their community. This makes the math relevant and easier to learn. ‘Motivation’ is one of the key factors in learning – when students choose to design a house, or study the habits and interests of their peers, they increase their commitment to learning the math.

All the Facts:

The ‘basic facts’ are essential to estimating and therefore play a huge role in developing number sense. In this program the facts are given meaning through the Problem Solving and Weekly Graph (Data Analysis) activities. The Power of Ten program operates on the assumption that all students, with very few exceptions, can learn their basic facts without using fingers, number lines, or charts as crutches. Timed tests are not employed as research shows that highly competitive timed tests can result in some students developing ‘avoidance’ and ‘learned helplessness’ which contributes to a fear of math. Expectations for accuracy are high without students needing to use counting aids. The Power of Ten cards provide a ‘visual tool’ that every student can use to create confidence in learning his/her facts without using fingers, charts or other calculators.

Games:

Games and puzzles are naturally interesting to almost everyone. Games are creative and ‘good’ games always involve some kind of problem solving and pattern making. The games using the Power of Ten cards (ten-frames) allow students to create a visual picture for the numbers to twenty that can be used to create patterns for the basic facts. For example 6 + 9 involves taking 1 from the 6, giving it to the 9 to create a 10 and then adding 10 + 5 to get 15.

Subtraction is very easy especially for the questions involving regrouping. For example 13 – 9 is imagined as 10 + 3 – 9 and now the 9 is subtracted from the 10 so the answer is 1 + 3 = 4.

As students learn more games they can make choices which creates commitment to their learning. The amount of time spent playing games is reduced as the students get older.

Weekly Graphs (and data collection):

Data is used to create a context of meaning for the basic facts and for decimals, fractions and percent in the intermediate and middle school years. Students who collect and analyse data see the relevance to understanding the basic operations and the use of decimal fractions, common fractions and percents for comparing data. For example the following data allows the study of many mathematical operations:

• Adding a number to 9 by asking, “How many students like apples?”
  (9 + 6 = ?)
  
  
• Adding 2 to a number, by asking, “How many students like bananas?”
  (2 + 3 = ?)
  
  
• Adding 1 to a number, by asking, “How many students like oranges?”
  (1 + 4 = ?)
  
  
• Adding friendly numbers (making tens), by asking, “How many girls voted?”
  (6 + 3 + 4 = 6 + 4 + 3 = ?)
  
  
• Adding friendly numbers (making tens), by asking, “How many boys voted?”
  (9 + 2 + 1 = 9 + 1 + 2 = ?)
  
  
• Learning differences of 2 or 1 by asking, “What is the difference of girls and boys who like bananas?” or “Compare the number of boys to the number of girls who like oranges.”
  (3 – 2 or 4 – 1)
  
  
• Next, connections could be made to All the Facts by doing all the questions involving 9, 1, 2 or friendly numbers and differences of 1 or 2. Further connections could be made to games by playing: Friendly Concentration, Friendly Match It, Friendly Fish, Power of Nine, or Salute for subtraction.

• “What fraction (or percent) of the students who like apples are girls?”
  6/15 = 2/5 = 0.4 = 40%
  
  
• “What fraction of the boys like apples”
  9/12 = 3/4 = .75 = 75%
  
  
• Other fractions, decimals or percents that could be studied, depending on what is asked include:
  15th, 5th, 12th, 13th, 25th
  
  
• Connections can also be made to bar graphs, circle graphs, double bar graphs, pictographs and probability.