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CHAPTER 8: EXPLORING NUMBERS AND OPERATION SENSE (TEACHING…
CHAPTER 8: EXPLORING NUMBERS
AND OPERATION SENSE
DEVELOPING ADDITION AND SUBTRACTION OPERATION SENSE
Physical Action involved Change Problems
Result unknown, change unkown or start is unkown
Join/ add to problems
separate/ take from problems: start with the whole
Part part who and compare problems: No physical action
whole unknown, one part unknown, both unknown
Problem difficulty
start part unknown is most difficult
Teaching Addition and subtraction
Contextual problems
Connected to life out side of school math
develop math modeling for the real world
Helpful for ELL students
Lesson built on context
Choosing Numbers for problems
Use relevent real world data to increase interest
Model- Based Problems
Students use base ten materials, Bar graphs number lines ect
"thinking Blocks" MATH APP
MULTIPLICATION AND DIVISION PROBLEM STRUCTURES
Equal Groups
Product unknown (Multiplication)
Croup Size Unknown (Partition Division)
Number of groups unknown (measurment division)
Comparison Problems
Array and area problems
Equal group
combination Proablesm
Not for introductory point
TEACHING MULTIPLICATION AND DIVISIONS
Often taught separately- Multiplication followed by division
teach about grouping
contextual problems
interesting problems
solve few problems and focus on the stratagie
symbolism for multiplication and division
Choosing numbers for problems
numbers should be with in students grasp
address what to do with remanders must be taught!!!!!!
Model based problems
work hands on with models
PROPERTIE OF MULTIPLICATION AND DIVISION
Commutative and associate properties
communatitve 3
8 = 8
3
6x(3x2) =(6x3)x2
zero and identity properties
anything times 0 equals 0
anything times 1 equals the number
Distributive Property
split either of the two factors in a multiplication problem into two or more parts. still be able to multiply it and get the same thing
4x9=(4x6)+(4x3)
division by zero
Sometimes students are told not allowed
STRATEGIES FOR SOLVING CONTEXTUAL PROBLEMS
Analyzing context problems
Thing about the answer before solving the problem
What is happening in this problem
is there any extra info we do not need
what will the answer tell us
will the answer be a small number or a large number
about what do you think the answer will be
Work a simpler problem
Subsititue small whole numbers
model the problem
write an equation that solves a simpler version
calculate
wrtie the answer in a comlete sentence
AVOID THE KEY WORD STRATEGY
MULTISTEP WORD PROBLEMS
students do one step problem and then come up with second step to problem
hidden question. Students come up with second question and other group has to figure out part two