Conceptual place value is defined as being able to flexibly increment and decrement numbers by tens and ones both on and off the decuple.
Give an example of incrementing a number by 10 off the decuple.
Give an example of decrementing a number by 1 on the decuple.
On page 78, the authors explain that teachers often take for granted that students can understand ones, tens, and hundreds without instruction. What are two examples of sophisticated tens thinking that students need to understand.
Bundling sticks are popsicle sticks organized into bundles of ten with some sticks left free of the bundles. On pages 79 – 81 the authors explain how to teach Conceptual Place Value. They start with bundling sticks, incrementing by tens off the decuple. Summarize the next steps for instruction.
On page 80, the authors explain why it is best to use groupable materials such as bundling sticks before using pre-grouped materials such as the Diene’s blocks found in your manipulatives kit. Why are the groupable materials necessary?
Copy the table on page 83 into your notes.
Explain why it is important to teach Conceptual Place Value before teaching the traditional algorithms.
Give a six-word summary of structuring numbers.
Combine and partition numbers without counting.
Being facile with addition and subtraction doesn’t necessarily mean adding and subtracting quickly. The authors give three aspects of facile addition and subtraction, describe and give an example of each.
Description
example
Knowledge of key number combinations and partitions
Part-whole constructions of numbers
Recognizing 7 as 3 and 4 or 5 and 2 or 3 less than 10.
Relational thinking
Recognizing a richly organized network of number combinations, partitions, and relationships
On page 53, why do the authors suggest that we need to explicitly teach structuring of numbers?
What are 2 manipulative that you can use to help students learn the structure of numbers?