TIPM3 November 16, 2010

What Children Should Know about 8 Minimal Skills Count to 8 Count 8 objects and know that the last number word tells how many Write the numeral 8 Recognize and read the numeral 8

More and less by 1 and 2 8 is one more than 7, one less than 9, two more than 6 and two less than 10 Spatial patterns for eight What Children Should Know about 8

More and less by 1 and 2 8 is one more than 7, one less than 9, two more than 6 and two less than 10 Spatial patterns for eight Anchors to 5 and 10: 8 is 3 more than 5 and 2 away from 10 Part-whole relationships: 8 is 5 and 3, 2 and 6, 7 and 1, and so on. Doubles: double 4 is 8 Relationship to the real world My brother is 8 years old, my reading book is 8 inches ling What Children Should Know about 8

Addition and Subtraction Problem Structures Categories that the students do not need to master Teachers need to know as part of Pedagogical content knowledge (PCK) Allows for proper sequencing to support student learning.

Main Ideas Two different approaches for developing operation meaning Word problems vs use of models Cognitively Guided Instruction Group and van De Walle support through word problems Parallel development of addition and subtraction

Important Ideas Avoid the phrase take away for subtraction. Instead use minus or subtract Addition is not defined as join and subtraction as remove There are joining action problems that can be classified as subtraction. There are remove problems that require addition.

Important Ideas 4 + [ ] = 9 (join, change unknown) This is a subtraction situation 9 – 4 = [ ] For large numbers like 4,376 + [ ] = 9,201 Subtraction must be used to solve How do you get children to see the equivalence of these equations?

More Important Ideas Strong tendency to use the equal sign as a symbol to precede the answer. The correct meaning of the equal sign is very difficult to develop Develop the idea of the equal sign as « the same as »

Most Importantly View subtraction as finding the missing part. Subtraction is used to name or find a part of the whole when the whole and one of the parts is known. When seeing 9 – 6, think of 6 and what number make 9?

Movie Time myeducationlab.com

Addition and Subtraction Problem Structures Join Problems Separate Problems Part-Part-Whole Problems Compare Problems Each structure has three numbers. Any one of the three numbers can be the unknown in the story problem

Join Problems Initial Change Result Use pennies and nickels to model the stories.

Join: Result Unknown Initial Change Result Sandra had 8 pennies. George gave her 4 more. How many pennies does Sandra have altogether.

Join: Result Unknown 8 Change Result Sandra had 8 pennies. George gave her 4 more. How many pennies does Sandra have altogether. Initial 4 12

Join: Change Unknown Initial Change Result Sandra had 8 pennies. George gave her some more. Now Sandra has 12 pennies. How many did George give her? 12 8 ?

Join: Initial Unknown Initial Change Result Sandra had some pennies. George gave her 4 more. Now Sandra has 12 pennies. How many pennies did Sandra have to begin with? ? 4 12

Join Problems: On Your Own Join, Result Unknown Join, Change Unknown Join, Initial Unknown Write an equation to show the solution.

Separate Problems Initial Change Result Any one of the three numbers can be the unknown in the story problem. In separate problems, the initial amount is the whole or the largest amount

Separate: Result Unknown Initial Change Result Sandra had 12 pennies. She gave 4 pennies to George. How many pennies does Sandra have now?

Separate: Change Unknown Initial Change Result Sandra had 12 pennies. She gave some pennies to George. Now she has 8 pennies. How many did she give to George?

Separate: Initial Unknown Initial Change Result Sandra had some pennies. She gave 4 pennies to George. Now Sandra has 8 pennies left. How many pennies did Sandra have to begin with?

Separate Problems: On Your Own Separate, Change Unknown Separate, Result Unknown Separate, Initial Unknown Write an equation to show the solution

Part-Part-Whole Problems Initial Change Whole Part There are two parts combined into one whole The combining can be a physical action or a mental combination. No meaningful distinction between the two parts in this part-part-whole situation.

Part-Part-Whole: Whole Unknown Initial Change Whole Part 1. George has 4 pennies and 8 nickels. How many coins does he have? 2. George has 4 pennies and Sandra had 8 pennies. They put their pennies into a piggy bank. How many pennies did they put into the bank?

Part-Part-Whole: Part Unknown Initial Change Whole Part 1. George has 12 coins. Eight of his coins are pennies. The rest are nickels. How many nickels does George have? 2. George and Sandra put their pennies into the piggy bank. George put in 4 pennies. How many pennies did Sandra put in?

Part-Part-Whole: On Your Own Whole Unknown Part Unknown Write an equation to show the solution. Thinking Blocks Model It

Compare Problems Initial Change Small set Large set Difference Compare problems involve the comparison of two quantities. The third amount does not exist but is the difference between the two amounts.

Compare: Difference Unknown Initial Change Small set Large set Difference George has 12 pennies and Sandra has 8 pennies. How many more pennies does George have than Sandra? 128

Compare: Difference Unknown Initial Change Small set Large set Difference George has 12 pennies and Sandra has 8 pennies. How many fewer pennies does Sandra have than George? 128

Compare: Larger Unknown Initial Change Small set Large set Difference 8 4 George has 4 more pennies than Sandra. Sandra has 8 pennies. How many pennies does George have?

Compare: Larger Unknown Initial Change Small set Large set Difference 8 4 Sandra has 4 fewer pennies than George. Sandra has 8 pennies. How many pennies does George have?

Compare: Smaller Unknown Initial Change Small set Large set Difference George has 4 more pennies than Sandra. George has 12 pennies. How many pennies does Sandra have? 12 4

Compare: Smaller Unknown Initial Change Small set Large set Difference Sandra has 4 fewer pennies than George. George has 12 pennies. How many pennies does Sandra have? 12 4