tipm3 november 16, 2010. what children should know about 8 minimal skills count to 8 count 8 objects...

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 Ideas4 + [ ] = 9 (join, change unknown)This is a subtraction situation9 – 4 = [ ]

For large numbers like4,376 + [ ] = 9,201Subtraction must be used to solve How do you get children to see the

equivalence of these equations?

More Important IdeasStrong 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 ImportantlyView 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?

128

?

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 UnknownJoin, Change UnknownJoin, 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 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 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 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 setLarge 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 setLarge set

Difference

George has 12 pennies and Sandra has 8 pennies. How many more pennies does George have than Sandra?

12 8

Compare: Difference Unknown

Initial

Change

Small setLarge set

Difference

George has 12 pennies and Sandra has 8 pennies. How many fewer pennies does Sandra have than George?

12 8

Compare: Larger Unknown

Initial

Change

Small setLarge 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 setLarge 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 setLarge 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 setLarge set

Difference

Sandra has 4 fewer pennies than George. George has 12 pennies. How many pennies does Sandra have?

12

4