Sept. 8, 2010

Earlier number systems can be used to help students understand the importance of place value.

Part Part Whole relationships

• The most fundamental concept you can teach to kids
• If students can understand how to break up numbers math will be easy/easier
  
• This is HUGE for students to undertand.
  
• There are different ways to represent numbers
• Example: 23 = 10 + 10 +3, 23 is the whole, 10, 10 and 3 are the parts that equal the whole
  

Ah-Ha Moment -

• I never realized how important it was for students to understand part part whole relationships, but that makes sense. Break up the numbers. Doing math is MUCH easier when you break up the numbers. Thinking about what I do when solving math problems, I break up the numbers. When I do that it's easier and much quicker for me. Every student is different and that means that they will have different approaches to solving math problems. When they use part part whole relationships, they are going to go about it differently.

Developing Whole-Number Place-Value Concepts pg 187 - 193

• Why is "base-ten language" important?
  5 tens + 3 ones is and example of "base-ten language"
  It is the base of our number system.
  Being consistent w/vocabulary and reinforces the vocabulary
  It helps students understand the concept of part part whole
  
  
• Explain three ways one can count a set of objects and how these methods of counting can be used to coordinate concepts and oral and written names for numbers.
  
  
  
  
  1. Counting by Ones -
     
  2. Counting by Groups and Singles - Example: "One, two, three, four, five bunches of ten and one, two, three singles." This method does not tell directly how many items there are. This counting must be coordinated with a count by ones before it can be a means of telling "how many."
  3. Counting by Tens and Ones -
     

• Describe the three types of physical models for base-ten concepts. What is the significance of the differences among these models?
  
  
  
  
  1. Base-Ten Models - a good base-ten model for ones, tens and hundreds is one that is proportional.
     
  2. Groupable Models - clearly reflect the relationships of ones, tens, and hundreds are those for which the ten can actually be make or grouped from the singles.
     
  3. PreGrouped or Trading Models - are commonly shown in textbooks are are commonly used in instructional activities.
     
  4. Nonproportional Models - these models can be used when students don't need to understand how ten units make a "ten" or by students who need to return to place-value concepts as they struggle w/more advance computations.

Reflection - How does the knowledge you have gained about place value impact your teaching of place value in your classroom?

• I've always known place value is important, but as I have learned more and more about place value I have found how important it is to teach place value using different approaches. The students in my classroom are all different and have different learning styles. Helping students understand place value can be difficult. Some students totally get it, some students kind of get it, and some students will pretend to get it. As an educator I try to teach place value in concrete, representatonal and abstract ways.

Draw 3 representations of 463

Set Models and Measurement Models

• Set - The answer must be a whole number. Example: counting discrete objects, groups, singles.
• Measurement - The answer is often not a whole number. Example: number line, distance, height, length.

Assignment for Next Week

• Read Van de Walle - pgs 167 - 170 - Helping Children Master the Basic Facts.
• Read Beckman - pgs 100 - 104
• Reflection of class - view reflection question on pg 5 of syllabus