MAE2240 Lecture Notes - Lecture 5: Commutative Property, Number Sense, Distributive Property
29 May 2018
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!WEEK!5!
Number!and!Algebra!
!
Number!and!Algebra!are!developed!together!as!each!enriches!the!study!of!the!other.!
Students!apply!the!number!sense!and!strategies!for!counting!and!representing!numbers.!
They!explore!the!magnitude!and!properties!of!numbers.!They!apply!a!range!of!strategies!for!
computation!and!understand!the!connections!between!operations.!!
• Proficiency!strand!-!understanding:!…partitioning!and!combining!numbers!flexibly,!
identifying!and!describing!the!relationships!between!addition!and!subtraction!and!
between!multiplication!and!division.!!
!
What!does!understand!operations!mean?!Select!operation,!combining!the!use!of!materials!
and!diagrams!to!represent!situations!that!involve!operation.!
!!
Children's!informal!thinking!
If!there!are!more!than!two!numbers,!add!them,!if!two!numbers!are!similar!in!magnitude,!
subtract!the!smaller!from!the!larger,!if!one!number!is!relatively!large!compared!to!the!
second!number,!divide.!If!the!division!answer!has!a!remainder,!cross!out!your!work!and!
multiply.!!
!
Different!types!of!maths!problems:!
Static:!nothing!changes!
• 'compare'!
• 'part/part!whole'!
Change:,,
• 'join!and!separate'!
• 'equalise'!
!!
Understand!operations!
Addition,properties:,
• Commutative!property!a!+!b!=!b!+!a!
• Associative!(a!+!b)+c!=!a+(b!+!c)!
Multiplication,properties:,
• Commutative!property!a!x!b!=!b!x!a!
• Associative!property!(a!x!b)!x!c!=!a!x!(b!x!c)!
• Distributive!property!a!x!(b!+!c)!=!(a!x!b)!+!(a!x!c)!
!!
Subtraction!is!the!inverse!of!addition,!a!common!subtraction!strategy!is!to!think,addition.,
However!subtraction!is!more!difficult.!Multiplication!and!division!are!the!inverse!of!each!
other.!
!!
Position!of!missing!information:!!
4!+!3!=!?,!Make!sure!you!vary!it!up!and!sometimes!the!start!is!unknown,!or!the!change!is!
unknown,!rather!than!it!always!being!the!result!unknown.!
"Researchers!have!defined!and!classified!multiplication!and!division!problems!in!a!number!
of!different!ways!-!that!is,!how!the!relationships!are!expressed!in!words"!(Chapin!and!
Johnson,!2000)!
!!
!
Document Summary
Number and algebra are developed together as each enriches the study of the other. Students apply the number sense and strategies for counting and representing numbers. They explore the magnitude and properties of numbers. They apply a range of strategies for computation and understand the connections between operations: proficiency strand - understanding: partitioning and combining numbers flexibly, identifying and describing the relationships between addition and subtraction and between multiplication and division. Select operation, combining the use of materials and diagrams to represent situations that involve operation. If there are more than two numbers, add them, if two numbers are similar in magnitude, subtract the smaller from the larger, if one number is relatively large compared to the second number, divide. If the division answer has a remainder, cross out your work and multiply. Addition properties: commutative property a + b = b + a, associative (a + b)+c = a+(b + c)
