Things you should think about

Remember that we teach for meaning! Teach with: problem solving in mind question asking in mind 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, but… Not all kids have the same experiences. Not all kids have the same maturity.

Make Connections Use open ended questions Make connections between operations Addition and subtraction Multiplication and Division

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

How to develop operational sense Multiple representations Various situations Various manipulatives. They don’t have to be fancy or store bought!!!

How to develop operational sense 1. Let them discover operations How things work 2. Make sure they understand properties  Commutative  Associative  Distributive  Identity  Zero

Understand operational meanings Operations relate to each other They can be used to understand math ideas They are the building blocks of later math meaning

Operations and Basic Facts It’s the chicken and the egg You can’t have one without the other Teach both simultaneously Make real life connections

Developing Number Sense When to use each operation The operations have meaning Operations are road signs on the highway.

How to teach number sense Find out what they know Pretest Ask questions Let them write Draw Explain

Can they count? How do they count? Make exaggerations for explaining why you use operations “Is 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?”

Counting How do they count? Forward… adding Skipping… multiplying Backwards… subtracting Grouping…division

Variety is the spice of life Ask lots of questions Ask: Does this make sense? Why? Help me understand How did you figure that out? Why did you do that?

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

General sequence of activities Concrete (touch, feel, make, act) Representational ( pictures, objects) Symbolic ( numbers, variables, sentences) Use this for EVERY new concept!!!!!

Models of operations This is the CGI concept Separation/ take away Start with a quantity Remove a specified quantity See what’s left Kids get confused if you say “Take Away” Say 8-3 ( eight minus three)

Models of operations Comparison Problems Two quantities Match them See what the difference is

Models of operations Multiplication and Division Use the same sequence of experiences Concrete Representational Symbolic Use lots and lots of representations

Representations Concretes Dots on the ceiling tile Slots in the blinds Slots in the radiator Fingers Eyes Shoes Ears Nose pickings

Models of operations Multiplication/ Equal Groups Certain number of groups All the same size How many in all Planning your wedding tables

Models of operations Comparisons/Multiplication Mike ran 25 miles, Chris ran 3 times as many

Models of operations Combinations Whiskey SodaWaterStraightRocks RumSodaWaterStraightRocks What do you get if you figure out the combinations?

The photo is not out of focus, it’s the combinations, silly!

Basic Fact Instruction Development begins in Kgn Kids work with the facts one or more years before they are expected to master them

They DON’T know Their Facts Kid may have an LD Understandings of operations haven’t been developed Teachers haven’t taught retrieval skills

Now what? Start where the kids are Build understanding/ operation sense Facts are commutative You only have to learn half of them!!!! Focus on remembering

Basic facts Help them organize their thinking 6x3=18 3x6=18 18/3=6 18/6=3 They know four facts!

Let them use tables Use the Burns book Look for patterns Color them Let kids discover patterns This is great for multiplication

Basic facts/Adding Look for patterns Look for the largest sum Write equations with it Circle sums of 5 it appears most often. Why? What number appears the most often in the table. Write the addition sentences for that sum

x You only have to learn half of the numbers!!!

Things to do with multiplication tables Use the Burns book!!! Patterns Skip count starting at 2. Color those blue Start 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?

Strategies Commutative: 6x7=42, so… 7x6=42 Missing number: 13-6=7 so…13-7=___ What’s missing?

Practice Daily 10 minutes at a time Start with ones you know Use cards Use dice Recall is the key