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quiz 3 mtt
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Terms in this set (36)
Identify and give examples of the three instructional models for fractions
1. Area model
2. Line model
3. Set model
Identify misconceptions children have with "fair shares"
- students don't understand that models of fractions need to have equal shares
- when students draw a block to show 3/4 for example they make 4 lines which ends up being fifths because the block has five little squares
Describe why the concept of "part - whole" is so difficult for students and how teachers can support their understanding
- children are told fractions are less than 1
- children can't think about the "part" and the "whole" at the same time
Explain why estimating and reasoning about fractions is so important
when students can estimate and reason w/ fractions they show they understand the concept of fractions
ex. which is more: 6/8 or 4/5
"i know 6/8 is two away from a whole and i know 4/5=8/10 so that's two away from a whole. tenths are smaller then eighths so 2/10 is smaller than 2/8 so 4/5 is larger"
Identify the harmful effects of teaching algorithms for operations with fractions
- algorithms for different operations get jumbled
- students can not determine the "reasonableness" of the result
Identify a supportive task for understanding the importance of a common denominator
students can use fraction strips to help understand common denominators
Describe how teachers can support children's understanding of decimals
using base ten blocks shows place value
Provide examples of representation and generalization in teaching algebra
generalization- making real world problems and having students create their own equations
representation- using physical models or having models with algebraic problems (picture with word problems)
What do we mean by a "high-quality" math task? And, how does it allow for differentiating instruction
a "high quality" math task is open ended to encourage multiple methods and representations...this allows students on many levels to participate in class
Explain and give examples of the three ways we can move children from arithmetic thinking to algebraic thinking
- kids need more experience with patterns (input/output)
- children need to expand their thinking of the equal sign (allow them to see the equal sign in different ways 8+4= _ + 5)
- generalize word problems (have students fill in their own variable instead of always giving it to them)
Explain why students struggle with the meaning of the equal sign
they think it's an operation rather than a symbol showing equivalence
Describe the instructional supports to help children understand the meaning of the equal sign
- true or false statements
- use of big numbers
- open number sentences
Identify and describe the levels of van Hiele's levels of geometric thought (first 3 levels)
1. visualization: determine the geometric shape
2. analysis: properties
3. informal deduction: interrelationships between figures (comparing)
Describe an activity that can support students' progressions through the first three levels of van Hiele's levels of geometric thought
Battleship- helps with grids
Identify and describe the four strands of geometry
- shapes and properties
- location
- transformation
- visualization
Describe hierarchical inclusion
counting and quantity principle that refers to understanding that all numbers preceding a number can be or are systematically included in the value of another selected number
Identify obstacles of the English count words for understanding mathematics
- what is eleven and twelve?
- what is "teen"
- what is "twen" (twenty)
Identify and provide examples of patterning, sorting, ordering, and one-to-one correspondence
pattern- repeated arrangment of numbers
sorting- similarities and differences
ordering- putting things in their correct place
1-1 correspondence- pair each number with an object
Differentiate between perceptual subitizing and conceptual subitizing
perceptual- recognizing the quantity of a small group of objects without using other mathematical processes (sees 5, understands its 5)
conceptual- recognizing smaller groups and adding them together such as two dots plus two = 4 dots (helps them advance to + and -)
Describe and identify the stages of learning to count
1. learning the sequence of the numbers and words
2. pointing to objects when saying the numbers
3. one-to-one correspondence
4. keeping track of counted objects
5. cardinality
Describe and identify the stages of learning to add
1. count all
2. count on
3. derived facts
4. memorized facts
Describe the instructional benefits of using a rekenrek
- ideal for building number sense
- concrete, physical object
- learning about relationships with numbers 5 and 10
Describe the instructional benefits of a ten frame
- quick images
- learn basic facts
- number sense
- solve + and - problems
Describe and identify ten-structured thinking
use of number 10 as a conceptual pivot point
Describe how a teacher can support children's ten-structured thinking
discussing multiple solution methods
Identify and write asymmetric and symmetric multiplication word problems
- Symmetric multiplication word problems involve area and have the same units
- Asymmetric multiplication word problems involve groups with different units
Describe unitizing and its importance for both place-value understanding and multiplicative thinking
- Unitizing is when children can think of a collection of objects as a "group"
- 12 donuts = 1 dozen
- helps students understand place value
Explain why children can solve asymmetric multiplication word problems without having to multiply
Skip counting
Counting by ones
Repeated addition
Identify supportive activities for solving symmetric multiplication word problems
Candy box research
How long? How many?
Multiplication rectangles (chart)
Identify geometric patterns in the multiplication table
Skinny on the outer frame
Fatter towards the bottom
Down and across gets bigger
Perfect squares towards the middle
Explain how teachers can support children's understanding of the distributive property
Use area models, blocks and cut them all different ways
Identify and write both types of division word problems
Partition division (Total is known, number of sets is known, want to know how many are in each set)
Measurement division (Total is known, how many are in each set is known, want to know how many sets)
Explain how the division word problem type prompts students in their choice of solution method
6 x ? = 24, prompt students to use repeated addition or skip counting
Explain the benefit of using division problems that have a remainder
- It models real life situations because in real life there is not always going to be "easy" or "nice" numbers.
- It prevents students from getting into the mindset that if there is a reminder then the problem "won't work" or "doesn't work"
Explain the instructional method of using base-ten blocks to support children's understanding of the long division algorithm
- Have students represent the factor with base ten blocks
- And then have them break it into however many groups for the other factor
Ask the students "How many _______ did each group get?"
Explain the idea of intellectual authority and its implications in teaching
- Allow kids to think about math themselves instead of just telling them what to do and giving them the answer
- Let them struggle with it and contemplate math
- Let them figure out their own algorithms
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