TIPM 3 November 16 2010 What Children Should

TIPM 3 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

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

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

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

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

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

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

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

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

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

Separate: Change Unknown Change Initial 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 Change Initial 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-Whole Problems Change Part Whole Initial • 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-whole situation.

Part-Whole: Whole Unknown Part Change Whole 1. George has 4 pennies and 8 nickels. Initial 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-Whole: Part Unknown Part Change Whole 1. George has 12 coins. Eight of his coins are Initial The rest are nickels. How many pennies. 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-Whole: On Your Own • Whole Unknown • Part Unknown • Write an equation to show the solution. • Thinking Blocks • Model It

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

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

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

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

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

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