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39 Cards in this Set

  • Front
  • Back
Join Result Unknown (JRU)
Tina had 5 toys. Alonzo gave Tina 3 more toys. How many toys does Tina have now?

level 1
Join Change Unknown (JCU)
Tina had 5 toys. Alonzo gave Tina some more toys. Now Tina has 8 toys. How many toys did Alonzo give Tina?

level 2
Join Start Unknown (JSU)
Tina had some toys. Alonzo gave Tina 3 more toys. Now Tina has 8 toys. How many toys did Tina start with?

level 4
Separate Result Unknown (SRU)
Tina had 8 toys. She gave Alonzo 3 toys. How many toys does Tina have now?

level 1
Separate Change Unknown (SCU)
Tina had 8 toys. She gave some toys to Alonzo. Now Tina had 5 toys. How many toys did Tina give Alonzo?

level 2
Separate Start Unknown (SSU)
Tina had some toys. She gave Alonzo 3 toys. Now Tina has 5 toys. How many toys did Tina have to begin with?

level 4
Part-Part-Whole:Whole Unknown (PPW:WU)
Lindsey has 14 green markers and 12 yellow markers. How many markers does she have in all?

level 1
Part-Part-Whole:Part Unknown (PPW:PU)
Lindsey has 26 markers. 14 are green and the rest are yellow. How many are yellow?

level 2
Compare Difference Unknown (CDU)
There are 8 read marbles and 5 yellow marbles. How many more read marbles than yellow marbles?

level 2
Compare Quantity Unknown (CQU)
There are 5 yellow marbles. There are 3 more red marbles than yellow. How many red marbles.
Compare Referent Unknown (CRU)
There are 8 read marbles. There are 3 more red marbles than yellow. How many more red than yellow. How many yellow marbles?

level 3
Multiplication (Groups of members = ?)
4 cars each have 6 students in them. How many students are there in all?
Measurement Division
(? of members =total) 24 students need to ride to the field trip with 6 students in a car. How many cars will by needed? (repeated subtraction, # of groups)
Partitive Division (groups of ? = total)
24 students need to ride in 4 cars with the same number of students in each car. How many students will be in a car? (# of members in each group)
Developmental Stages of Math
Direct Modeling
Counting
Derived Facts
Direct Modeling
Distinguished by the child's explicit physical representation of each quantity in a problem and the action or relationship involving those quantities before counting the resulting set.
Counting
The child recognizes that it is not necessary to actually construct and count sets. Physical objects (tally marks, fingers, objects) are used to keep track of counts rather than to represent objects in the problem.
Derived Facts
Solutions are based on understanding relations between numbers.
Strategies for JRU and PPW:WU
Direct Modeling: joining all
Counting: counting on from first, counting on from larger
Strategies for SRU
Direct Modeling: separating from
Counting: counting down
Strategies for PPW:PU
Counting: counting down, counting on to
Strategies for JCU
direct modeling: joining to
Counting: counting on to
Strategies for CDU
Direct modeling: matching
Strategies for JSU
Trial and error
representational models
enactive
iconic
symbolic
enactive representation
tangible, physical, manipulative
iconic representation
moving from tangible to a written representation of the physical
symbolic representation
begin using symbols
3 issues students struggle with when they get to algebra
place value
fractions
number sense
Why use different problem types?
-help see where the child is so the teacher can help them progress
-different difficulty levels
-help plan lessons
-variety
quotity
ability to hold a number in their head
Direct Modeling Level: characteristics
-follows time sequence in problem
-does not have quotity
-has one to one correspondence (1 number to 1 object)
Counting Level: characteristics
-quotity-holding a number
-eventually able to move the order of the numbers in the problem (ignoring sequence)
-simultaneous counting-one finger/counter can also mean '8' etc.
Derived Facts Level:characteristics
-using what you know to solve what you don't know
-decomposing-breaking apart the numbers
-compensating-changing the numbers in a useful way
-doubling (could be a type of compensating or decomposing depending on how it is used)
math
the science of pattern and order
Principles of Developing Mathematical Thinking: Building Mathematical Understanding
1.Take students' ideas seriously.
2. Press students conceptually.
3. Encourage multiple strategies.
4. Address misconceptions
5. Focus on the structure of mathematics
Models: Multiply/Divide
ratio table
partial quotients/products
open area model
repeated addition
repeated subtraction
decomposition
compensation
Models Addition/Subtraction
Base 10
Tree diagrams
Arrow Language
Number lines
Partial sums/differences
decomposition
compensation
How often to assess timed math facts.
What is fluent?
Every 1-2 weeks.
1 every 3 seconds