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What is the primary purpose of drill of basic
facts?
Kids have to be able to know their basic facts in order to do higher level math skills. If kids do not know their basic facts, they will be very slow later on. TERM 2
Identify basic fact strategies for addition
(adding to 10, doubles, counting on,
commutativity)
DEFINITION 2 Adding to 10: 8+5= (8+2)+3= 10+3=13 Doubles: Knowing that 4+4=8 6+6=12 7+8 = 7+7+1 = 15 Counting on: 2+6= 678 Commutativity: Children should understand that it does not matter which number comes first in an addition problem. 3+4 provides the same answer as 4+ TERM 3
Identify basic fact strategies for subtraction
(double, using 0 and 1, counting on, counting
back)
DEFINITION 3 Doubles: 16-8= 8+ = 16 8+8=16 so 16-8=8 Using 0 and 1: Once students know how to add 0 and 1, it is easy for them to subtract 0 and 1. Counting on: 8-6= 678 Counting back: 9- 2= 987 TERM 4
Identify basic fact strategies for multiplication
(commutativity, repeated addition, skip
counting, splitting the product into known
parts)
DEFINITION 4 Commutativity: Students should understand that it does not matter which numbers comes first in a multiplication problem. 3 x 4 provides the same answer as 4 x 3 Repeated addition: 4 x 5 = 5+5+5+5=20 Skip counting: 4 x 5 = 5, 10, 15, 20 Splitting the product into known parts: 9 x 8 = 8 x 8 = 64 + 8 = 72 TERM 5
How is the calculator a valuable
computational tool?
DEFINITION 5 It facilitates problem solving It relieves tedious computation It focuses attention on meaning It removes anxiety about computational failure It provides motivation and confidence It facilitates a search for patterns It supports concept development It promotes number sense It encourages creativity and exploration
Spending time on mental computation is
important because
Its useful. of all calculations done by adults are done mentally. It provides a direct and efficient way of doing many calculations. It is an excellent way to develop critical thinking and number sense and to reward creative problem solving. It contributes to increased skill in estimation. TERM 7
Strategies in teaching mental computation
DEFINITION 7 Encourage students to do computations mentally Check to learn what computations students prefer to do mentally Check to learn if students are applying written algorithms mentally Include mental computation systematically and regularly as an integral part of instruction Keep practice sessions shortsperhaps 10 minutes at a time TERM 8
Four phases for the classroom assessment
process (in sequential order)
DEFINITION 8
- Plan assessment 2. Gather evidence 3. Interpret evidence
- Use results TERM 9
Know the difference between mental
computation and estimation
DEFINITION 9 With mental computation, we want students to get the correct answer in their head. With estimation, we just want kids to get close. TERM 10
The most difficult computational algorithm is
DEFINITION 10 Division
Prerequisites for numerical operations
Counting expertise: forward, backward, 2s, 3s, etc. Experience with concrete situations Familiarity with problem- solving situations: I dont know the answer, but I can work it out! Experience in using language to communicate math ideas TERM 17
Name and demonstrate two common
algorithms for subtraction with regrouping
DEFINITION 17 Decomposition algorithm. This is the one we use in the United States. Equal-additions algorithm: this is used in Europe and South America TERM 18
Common myths about using calculators in the
classroom (dispel myths)
DEFINITION 18 Calculator use does not require thinking Use of calculators will harm students math achievement Computations with calculators are always faster Calculators are useful only for computation TERM 19
Why is division so hard for kids?
DEFINITION 19 It combines several math algorithms. Kids must be able to do multiplication, subtraction, and division. Computation begins at the left instead of at the right. Interactions move from one spot to the other. There is a lot of jumping around. Trail quotients may not be successful the first or second tries. TERM 20
Why should the concept of remainders be
introduced to students early?
DEFINITION 20 Students should understand that real-life problems do not always come out even and things cannot always be divided evenly.
Major Shifts in Assessment Practices (look for
chart in book)
Shifts in assessing to make instructional decisions o Toward integrating assessment with instruction o Toward using evidence from a variety of assessment formats and contexts o Toward using evidence of every students progress toward long-range planning goals Shifts in assessing to monitor students progress o Toward assessing progress toward mathematical power o Toward communicating with students about performance in a continuous, comprehensive manner o Toward using multiple and complex assessment tools o Toward students learning to assess their own progress Shifts in assessing to evaluate students achievement o Toward comparing students performance w/performance criteria o Toward assessing progress toward mathematical power o Toward certification based on balanced, multiple sources of information o Toward profiles of achievement based on public criteria TERM 22
How are CCS in Math different than the
original ILS?
DEFINITION 22 Define specific grade levels for certain tasks Define specific tasks the kids should be able to do Includes math processes TERM 23
Compatible numbers in estimating
DEFINITION 23 With compatible numbers, you look for sets of numbers that are easily computed. TERM 24
George Polya model for problem-solving
DEFINITION 24 Understand the problem Devise a plan for solving it Carry out your plan Look back to examine your solution TERM 25
Front-end estimation
DEFINITION 25 In front-end estimation, you only use the number with the highest place value and make all the number behind it a 0. Then you add them up. For example, 38+27+62+75. 30+20+60+70=
