Operations: Meanings and Basic Facts

Operations: Meanings and Basic FactsThings you should think about

Remember that we teach for meaning!Teach with problem solving in mindTeach with question asking in mindMake sure to ask How did you get that?What were you thinking?How can you show me what you know?

Counting is ok!Counting is a basic thing that kids come to school with, butNot all kids have the same experiences.Not all kids have the same maturity.

Make ConnectionsBe open ended in your questioning.Let children make connections between operationsAddition and subtractionMultiplication and Division

Crucial Point!Understanding of basic operations provides the foundations of all later work!

How to develop operational senseUse multiple representationsUse a variety of situationsUse a variety of manipulatives.They dont have to be fancy or store bought!!!

How to develop operational senseLet them discover operationsHow things workMake sure they understand propertiesCommutativeAssociativeDistributiveIdentityZero

Understand operational meaningsHow operations relate to each otherHow they can be used to understand math ideasHow operations lead to building blocks of later math meaning

Operations and Basic FactsIts the chicken and the eggYou cant have one without the otherYou have to teach both simultaneouslyMake real life connections all the way through

Developing Number SenseIts important to know when to use each operationThe operations have meaningThink about them as if they were road signs on the highway.

How to teach number senseFind out what they knowPretestAsk questionsLet them writeDrawExplain

Can they count?How do they count?Make exaggerations for explaining why you use operationsIs this the best way to do this?Would you rather go play or count to 10,000?How else could we make this go more efficiently?

CountingHow do they count?Forward addingSkipping multiplyingBackwards subtractingGroupingdivision

Variety is the spice of lifeAsk lots of questionsAsk: Does this make sense? Why? Help me understandHow did you figure that out?Why did you do that?

Talk to people!!!!Have kids explainUse the summarizers we learnedHave them see if they can find others who agree.Have them solve disagreements mathematically. Pictorially

General sequence of activitiesConcrete (touch, feel, make, act)Representational ( pictures, objects)Symbolic ( numbers, variables, sentences)

Use this for EVERY new concept!!!!!

Ask me about teaching perimeterFlatsDesksWallsDots on the tilesFloor tiles

Write the formulaHow did you get the answerDo this over three roomsWhat did you use to measureModels of operationsThis is the CGI conceptSeparation/ take awayStart with a quantityRemove a specified quantitySee whats left

Kids get confused if you say Take AwaySay 8-3 ( eight minus three)

Models of operationsComparison ProblemsTwo quantitiesMatch themSee what the difference is

Models of operationsMultiplication and DivisionUse the same sequence of experiencesConcreteRepresentationalSymbolicUse lots and lots of representations

Use lots and lots of representationsRepresentationsConcretesDots on the ceiling tileSlots in the blindsSlots in the radiator

FingersEyesShoesEarsNose pickings

Models of operationsMultiplication/ Equal GroupsCertain number of groupsAll the same sizeHow many in all

Planning your wedding tables

Models of operationsComparisons/MultiplicationMike ran 25 miles, Chris ran 3 times as many

Models of operationsCombinations

WhiskeySodaWaterStraightRocksRumSoda

Water

Straight

Rocks

What do you get if you figure out the combinations?

The photo is not out of focus, its the combinations, silly!Basic Fact InstructionDevelopment begins in KgnKids work with the facts one or more years before they are expected to master them

They DONT know Their FactsKid may have an LDUnderstandings of operations havent been developedTeachers havent taught retrieval skills

Now what?

Start where the kids areBuild understanding/ operation senseFacts are commutativeYou only have to learn half of them!!!!Focus on remembering

Basic factsHelp them organize their thinking6x3=183x6=1818/3=618/6=3They know four facts!Let them use tablesUse the Burns bookLook for patternsColor themLet kids discover patterns

This is great for multiplication

+01234567890110210310410510610710810910Basic facts/AddingLook for patternsLook for the largest sumWrite equations with itCircle sums of 5 it appears most often. Why?What number appears the most often in the table. Write the addition sentences for that sum

x0123456789000000000001012345678920246810121416183036912151821242740481216202428323650510152025303540456061218243036424854707142128354249566380816243240485664729091827364554637281You only have to learn half of the numbers!!!Things to do with multiplication tablesUse the Burns book!!!PatternsSkip count starting at 2. Color those blueStart at 4. Color every 4 pink. What do you notice?Start at 5. Color every 5 orange.Start at 10. Circle every 10 in black. What do you see? How did it work? How does the table work?

StrategiesCommutative:6x7=42, so 7x6=42Missing number:13-6=7 so13-7=___Whats missing?

Practice Daily10 minutes at a timeStart wit hones you knowUse cardsUse diceRecall is the key