Operations: Meanings and Basic Facts

1. Operations: Meanings and Basic Facts Things you should think about

2. Remember that we teach for meaning! • Teach with problem solving in mind • Teach with question asking in mind • Make sure to ask • “How did you get that?” • “What were you thinking?” • How can you show me what you know?”

3. 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.

4. Make Connections • Be open ended in your questioning. • Let children make connections between operations • Addition and subtraction • Multiplication and Division

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

6. How to develop operational sense • Use multiple representations • Use a variety of situations • Use a variety of manipulatives. • They don’t have to be fancy or store bought!!!

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

8. Understand operational meanings How operations relate to each other How they can be used to understand math ideas How operations lead to building blocks of later math meaning

9. Operations and Basic Facts • It’s the chicken and the egg • You can’t have one without the other • You have to teach both simultaneously • Make real life connections all the way through

10. Developing Number Sense • It’s important to know when to use each operation • The operations have meaning • Think about them as if they were road signs on the highway.

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

12. 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?”

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

14. 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?

15. 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

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

17. Ask me about teaching perimeter • Flats • Desks • Walls • Dots on the tiles • Floor tiles • Write the formula • How did you get the answer • Do this over three rooms • What did you use to measure

18. 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)

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

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

21. 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

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

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

24. Models of operations • Combinations What do you get if you figure out the combinations?

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

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

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

28. 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

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

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

32. 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

33. You only have to learn half of the numbers!!!

34. 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?

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

36. Practice Daily • 10 minutes at a time • Start wit hones you know • Use cards • Use dice • Recall is the key