EDE 4123 Test 1
What are the NCTM process standards?
-Problem solving -Reasoning and proof -Connections -Communications -Representations
Compatible Numbers
Looking for two or three compatible numbers that can be grouped to equal benchmark values.
What are the three methods of teaching basic facts?
Memorization, Explicit Strategy Instruction, & Guided Invention
What is computational estimation?
Mental computation with at least two estimated quantities. Not a guess.
What are groupable models?
Unifix cubes, paper clips, and multilink cubes.
· What are the names of the various parts of addition, subtraction, multiplication, and division number sentences?
· Addition- addend + addend=sum · Subtraction- Minuend - subtrahend=difference · Multiplication- factor x factor = product · Division- dividend /divisor = quotient
Commutative Property of Addition
· Can switch the order of the addends and the sum is the same.
What is Cardinality Principle?
the last counting word stated indicates the quantity in the set.
List the 3 ways of counting sets of objects:
· Counting by ones · Counting by groups of tens and ones. · Counting with non-standard base-10 groupings.
What are the Don'ts for teaching Basic Facts?
· DO NOT use lengthy timed tests. · DO NOT use public comparisons of mastery. · DO NOT proceed through facts in order from 0 to 9. · DO NOT work on all facts all at once. · DO NOT move to memorization too soon. · DO NOT use facts as a barrier to good mathematics. DO NOT use fact mastery as a prerequisite forcalculator use
What are the types of multiplication problems?
· Equal groups · Multiplicative comparison · Product of measures · Combinations
What activities did we do in class to promote place value development?
· Equivalent representations · Models for Multi-digit numbers
What are the Do's for teaching Basic Facts?
· Focus on self-improvement · Drill in short time segments · Work on facts over time · Involve families · Make drill enjoyable · Use technology · Emphasize the importance of quick recall of facts
Associative Property of Addition
· 3 addends in different order still have the same sum.
Identity Property (Zero Property)
· Adding or subtracting zero to a quantity doesn't change the sum
Zero Property
0 sets of anything is 0 or any number of sets of 0 size is still 0.
List the digits in the order in which students should learn to write them? What is this based on?
1, 7, 4, 2, 5, 3, 6, 9, 0, 8. It's based on the numbers that are easiest to write and it moves to the harder ones. Lines, curves, circles. Based on motor skills
What is computational fluency?
Being able to do computations (basic operations) fluently. (quickly correctly, don't have to think about process). Students being able to have addition and subtraction strategies that they can use easily when they need to. This helps students be able to use alternative strategies mentally.
Rounding
Estimating all numbers to the same place value. Decide what the number is closer to.
NCTM Content Standards
Number and operations algebra geometry measurement data analysis and probability.
· Explain what a Basic Fact is.
Relationship in which the two parts are less than 10
How does the Number of the Day routine promote place value understanding?
Students see the how the number can be used in context as well as it being represented multiple ways through symbols, words, and place value language.
Invented Strategies
Students use any strategy other than the traditional algorithm that does involve physical models. Students use written records and some mental models.
Direct modeling
Students use manipulatives or drawings along with counting to directly represent the meaning of operation or story problem.
Traditional Algoithms
Students use rules and procedures for solving a problem after they understand the math behind the problem. Students prove their results using base-10 models.
Front end
The frontmost numbers are added or subtracted. Then an adjustment can be made by taking in consideration the right digits.
Distributive Property
ax(b+c)= axb+axc
What are the three developmental phases towards computational fluency?
direct modeling, invented strategies, and traditional algorithms
What are the strategies for computational estimation?
front end, rounding, and compatible numbers
What is number sense?
· Good intuition about numbers and their relationships. Develops gradually as a result of exploring numbers, visualizing them in variety of contexts, and relating them in ways that are not limited to traditional algorithms. · Number of the day activity, place value activities, equivalent representations
· Explain the three differences between invented strategies and traditional algorithms
· Invented strategies are number oriented rather than digit oriented. This means that when students use traditional algorithms, they think of the just the number instead of considering the place value. For example, in the problem 67+39. Students using the traditional algorithm would think about 6+4 instead of 60+40 when using invented methods. · Invented strategies are left-handed rather than right-handed. This means that invented strategies look at the larger digits to the left rather than the smaller digits to the right. For example, when using traditional algorithms, students would stack the digits and add the numbers to the right first, then the larger numbers to the right. This is the opposite for invented strategies. · Invented strategies are a range of flexible options rather than "one right way." Invented strategies allow students to use the methods that makes the most sense for what numbers are being used. Traditional algorithms use only one method for solving a particular kind of problem.
What are the types of addition and subtraction problems?
· Join Problems · Separate problems · Part-part-whole · Compare
Explain why "key words" should NOT be taught
· Make students forget about reading the context of the problem · Are misleading · Many problems do not have key words · Key words do not work with two-step or more advanced problems.
Associative Property of multiplication
· Multiplying 3 factors in any order results in the same product.
Identity Property
· Multiplying by 1 doesn't change the identity if the number.
List the skills/concepts that are taught through the Shapes of Numbers activity
· Part-part-whole relationships with numbers greater than 5. · Students see all the ways a number can be created by adding two digits. · Even and odd numbers
What are the types of division problems?
· Partition · Measurement
What are the necessary behaviors associated with counting?
· Producing the standard list of counting word in order · Connecting this sequence in a one-to-one manner with the items in the set being counted · Assigning each item counted one and only one counting word.
· How should multiplication be introduced to students?
· Start with combinations problems · Mickey mouse and flowers · To learn specific facts then learn foundational facts.
Memorization
· Teacher moves from presenting concepts of addition and multiplication straight to memorization of acts without developing strategies.
Guided Invention
· Teacher sets up tasks so students can see the number relationships. Then the students decide a strategy that works the best for the task. Derived facts.
Explicit Strategy Instruction
· Teacher shows students a strategy then they have students explore and practice using them. Teachers should use explicit strategy instruction as a way to support student thinking and should not be something for the students to memorize.
List examples of the three kinds of Base-10 Models:
· Unifix cubes · Base 10 blocks · Counters
List the 3 stages of counting:
· Unitary · Base 10 · Equivalent
Explain why and how ten frames should be used, stating specific groups of Basic Facts for Addition.
· Used with 10 frame facts and make a 10 strategy
How are place value concepts evident in the 1-100 chart?
· We looked across and down the column. We talked about how the ones and tens increased.
Commutative Property of multiplication
· can switch an multiplication problem and get the same answer.