Math Practices K-8 Students Should Able to:
Using concrete objects or drawings to think about and solve problems.
What is an example of - the mathematical practice of making sense of problems and persevere in solving them?
A national assessment conducted at regular intervals important for measuring overall improvement.
What is "National Assessment of Education Progess" (NAEP)?
This Progression is about understanding and using numbers. It underlies Operations and Algebraic Thinking as well as Number and Operations in Base Ten. It begins with early counting and telling how many in one group of objects. Addition, subtraction, multiplication, and division grow from these early roots. From its very beginnings, this Progression involves important ideas that are neither trivial nor obvious; these ideas need to be taught, in ways that are interesting and engaging to young students.
What are Counting and Cardinality and Operations and Algebraic Thinking?
Observation, interview probes, writing (journals or tests)
What are examples of effective strategies for assessing?
*Visualize, *look for patterns, *predict and check for resonableness, *formuate conjectures and justify claims, *create a list, table or chart, *simplify or change the problem, *write an equation
What are problem solving strategies?
Explain the relationship between quantities in problem situations.
What is an example of -- being able to reason abstractly and quantitatively?
Collaborate, construct, explore, formulate, justify, predict
What are examples of some verbs used in "doing mathematics"?
Add To with Result Unknown; Take From with Result Unknown; and Put Together/Take Apart with Total Unknown and Both Addends Unknown. The numbers in these problems involve addition and subtraction within 10. Students represent these problems with concrete objects and drawings, and they find the answers by counting
What are the three kinds of problem situations for students in Kindergarten to develop?
This type assessment does not assess the four elements of fluency.
What are timed tests?
Foundational facts: 2, 5, 0, 1; nifty nines; derived multiplication fact strategies; arrays; doubling; close facts are all examples of
What are reasoning strategies for multiplication facts?
Justify conclusions in a way that is undertandable to teachers and peers.
What is an example of-- Constructing viable arguments and critique the reasoning of others?
These are the elements necessary to have: conceptual understanding, procedural fluency, perservance and productive disposition.
What is "mathematical proficiency"?
Add To with Start Unknown
Take From with Start Unknown
Compare with Bigger Unknown using “fewer” language (mis- leading language suggesting the wrong operation)
Compare with Smaller Unknown using “more” language (mis- leading language suggesting the wrong operation)
What are the problem types that Grade 1 students should work with, but need not master?
Conceptual understanding and procedural fluency, strategic competence and adaptive reasoning, productive disposition
What should be assessed?
direct modeling,
invented strategies, and
standard algorithms
What are three types of computational strategies?
Shift viewpoints and see things as single objects or as made up of multiple objects.
What is an example of -- looking for and making use of structure?
These procedures with connections tasks and doing mathematics tasks engage students in productive struggle.
What are high-levels of "cognitive demand"?
Fluently add and subtract within 20 using mental strategies. Know from memory all sums of two one-digit numbers by the end of this grade.
What is Grade 2?
Consists of five levels and assesses a student's ability in three domains...
What is the "Number Knowledge Test" (NKT)?
More comutational proficiency is gained and these are some of the positive benefits: students make fewer errors; less reteaching is required; students develop number sense; invented strategies are the basis for mental computation and estimation...
What are benefits of invented strategies?
Assessing strategies to see if it/they make/s sense.
What are the examples of -- looking for and expressing regularity in repeated reasoning?
Without universal screening there is no ...
What is "Response to Intervention" (RTI)?
In this grade, students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit multiplying and related quotients. These skills and understand- ings are crucial; students will rely on them for years to come as they learn to multiply and divide with multi-digit whole number and to add, subtract, multiply and divide with fractions and with decimals. Note that mastering this material, and reaching fluency in single- digit multiplications and related divisions with understanding,may be quite time consuming because there are no general strategies for multiplying or dividing all single-digit numbers as there are for addition and subtraction. Instead, there are many patterns and strategies dependent upon specific numbers. So it is imperative that extra time and support be provided if needed.
What is the description of progression in the 3rd grade?
One is the first step in a prevention and intervention model and is brief, efficient and inexpensive.
The other is administered to provide information, in the process of formative assessment, regarding the effectiveness of an intervention.
What is the difference between screening measures and progress monitoring measures?
Use area models in context; use open array - a semi-concrete representation of the area model; develop the written record such as partial products and lattice multiplication
What are strategies for teaching standard algorithms for multiplication?