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39 Cards in this Set
- Front
- Back
Join Result Unknown (JRU)
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Tina had 5 toys. Alonzo gave Tina 3 more toys. How many toys does Tina have now?
level 1 |
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Join Change Unknown (JCU)
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Tina had 5 toys. Alonzo gave Tina some more toys. Now Tina has 8 toys. How many toys did Alonzo give Tina?
level 2 |
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Join Start Unknown (JSU)
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Tina had some toys. Alonzo gave Tina 3 more toys. Now Tina has 8 toys. How many toys did Tina start with?
level 4 |
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Separate Result Unknown (SRU)
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Tina had 8 toys. She gave Alonzo 3 toys. How many toys does Tina have now?
level 1 |
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Separate Change Unknown (SCU)
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Tina had 8 toys. She gave some toys to Alonzo. Now Tina had 5 toys. How many toys did Tina give Alonzo?
level 2 |
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Separate Start Unknown (SSU)
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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 |
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Part-Part-Whole:Whole Unknown (PPW:WU)
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Lindsey has 14 green markers and 12 yellow markers. How many markers does she have in all?
level 1 |
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Part-Part-Whole:Part Unknown (PPW:PU)
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Lindsey has 26 markers. 14 are green and the rest are yellow. How many are yellow?
level 2 |
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Compare Difference Unknown (CDU)
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There are 8 read marbles and 5 yellow marbles. How many more read marbles than yellow marbles?
level 2 |
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Compare Quantity Unknown (CQU)
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There are 5 yellow marbles. There are 3 more red marbles than yellow. How many red marbles.
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Compare Referent Unknown (CRU)
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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 |
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Multiplication (Groups of members = ?)
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4 cars each have 6 students in them. How many students are there in all?
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Measurement Division
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(? 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)
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Partitive Division (groups of ? = total)
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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)
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Developmental Stages of Math
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Direct Modeling
Counting Derived Facts |
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Direct Modeling
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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.
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Counting
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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.
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Derived Facts
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Solutions are based on understanding relations between numbers.
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Strategies for JRU and PPW:WU
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Direct Modeling: joining all
Counting: counting on from first, counting on from larger |
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Strategies for SRU
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Direct Modeling: separating from
Counting: counting down |
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Strategies for PPW:PU
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Counting: counting down, counting on to
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Strategies for JCU
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direct modeling: joining to
Counting: counting on to |
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Strategies for CDU
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Direct modeling: matching
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Strategies for JSU
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Trial and error
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representational models
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enactive
iconic symbolic |
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enactive representation
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tangible, physical, manipulative
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iconic representation
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moving from tangible to a written representation of the physical
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symbolic representation
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begin using symbols
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3 issues students struggle with when they get to algebra
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place value
fractions number sense |
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Why use different problem types?
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-help see where the child is so the teacher can help them progress
-different difficulty levels -help plan lessons -variety |
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quotity
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ability to hold a number in their head
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Direct Modeling Level: characteristics
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-follows time sequence in problem
-does not have quotity -has one to one correspondence (1 number to 1 object) |
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Counting Level: characteristics
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-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. |
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Derived Facts Level:characteristics
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-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) |
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math
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the science of pattern and order
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Principles of Developing Mathematical Thinking: Building Mathematical Understanding
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1.Take students' ideas seriously.
2. Press students conceptually. 3. Encourage multiple strategies. 4. Address misconceptions 5. Focus on the structure of mathematics |
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Models: Multiply/Divide
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ratio table
partial quotients/products open area model repeated addition repeated subtraction decomposition compensation |
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Models Addition/Subtraction
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Base 10
Tree diagrams Arrow Language Number lines Partial sums/differences decomposition compensation |
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How often to assess timed math facts.
What is fluent? |
Every 1-2 weeks.
1 every 3 seconds |