Math K-6 Competency 1

A student verbally counts, but not necessarily in order.

There are 5 cars. There are 3 on a yellow garage. How many more cars are on the purple garage? 3+?=5

Used to Teach...Fraction concepts, area and perimeter, ratio and proportions

Assessment Choice: Paper-and-pencil traditional test; competition; checklist and observation

Used to Teach...Surface area and volume, nets

Assessment Choice: Individual projects involving fraction models or whole class projects such as Kleenex Box Building

Equal Groups, Multiples (skip counting), Array (area), Multiplicative Comparison, Combinations (cartesian products)

"Three rows of three makes nine."

Equal Groups, Repeated subtraction, Arrays (area), Multiplicative comparison, Combinations, Division with remienders

A 3rd teacher using modeling to teach mult. Here we have 3 sets with 4 in each set. How many do we have altogether?

CRA stands for concrete, representation, abstract

A teacher gives a unit exam to measure outcomes and the effectiveness of instructional strategies.

Tiered Ability Grouping is...

data that used to determine where a student is in relation to a skill or topic; to make adjustments; ongoing process.

Representation use pictures, graphics and charts

Before starting a science unit, a teacher gives a quick assessment to determine students’ prior knowledge of concepts.

Assessment Choice: Written report; oral report; explain to another student; teach the class; create visual; observation

Flexible Grouping: Groups change from day to day and even within a class period.

6 balls were on the ground. He picked some of them. There were 3 balls still on the ground. How many balls did he take?

The count of objects in the subset as it relates to the defined whole. Whatever value is determined as one set.

Require reasoning, planning, and a higher level of thinking. Draw conclusions, cite evidence, develop argument

Solving problems using a correct method and arriving at the correct answer.

Student ability to quickly identify a number of items in a small group without having to count them...

Help make sense of facts that might be hard to memorize. Students decompose one of the addends to make a 10 from other

Used to Teach...Area and perimeter, probability

Models: (Concrete, Pictorial, Mental Images, Language)>>Symbols

Exploring efficient strategies for finding the correct answer. They can give a correct answer as an automatic response.

Choosing and explaining different strategies for arriving at a correct answer. Relates to student’s deep understanding

Math's fluency components are rate, accuracy, automaticity and flexibility.

assessment other than a standard paper-and-pencil test. Ex. performance assessment, observation, a recitation, project

A fourth-grade teacher wishes to assess her students' fluency with multiplication facts.

A teacher is checking on students as they work, intervening when necessary, uses this data to make instruc. decisions.

"4 jumps of three lands on 12."

Used to teach...Probability, ratio and proportion

Memorizing multiplication facts in third grade is which level of thinking of Webb's Depth of Knowledge?

Ex. "Two groups of three is six."

Number sense, Grouping, Array, Area and Number Line.

Used to Teach...Volume and surface area, addition fact families, multiplication fact families

Working toward quick recall of a math fact. Students who are fluent in math can respond to an answer at a quick rate.

The ability to process info without getting stuck on low-level details is an example of which component of math fluency?

Used to teach...Equivalent fractions, operations on fractions, decimals, percents

Measuring and recording data and producing graphs of relevant variables is which level of thinking of Webb's D.K?

______________is repeatedly performing the same process by using the result, or output,...

At the end of the year students take the FSA. The state uses the scores for accountability measures. student vs criteria

A student can count out a small group of objects and understands that counting leads to how many.

helps students visualize parts of the whole.

Interest Grouping: Groups of students based on student interest.

Used to teach...Solving equations, simplifying expressions

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?

The ______________states that if A is related to B and B is related to C in that same way, then A is also related to C.

Assessment Choice: Projects with manipulatives

Range of formal and informal assess or checks by the teacher bef, dur, after the learn. proc. in order o modify instruc

Specific method of computation that is conventionally taught for solving particular mathematical problem.

Learning progressions: how a student moves from a simple understanding of a concept or skill to more complex...

Darrell has seven pairs of socks. Three pair are blue, and the rest are white. How many pairs of socks are white?

"9 by 8 covers 72 spaces."

There are 3 bags with 6 plums in each bag. How many plums are there in all? 3 x 6 = ?

method not limit to trad tests used to help measure the extent of a student's acad accomplish, strengths, and weaknesses

The NAEP is an exam for data purposes only to compare students’ reading scores across the U.S. Student vs Population

A student can count a small group of objects accurately.

The tube is 18 feet tall. The table is 6 feet tall. What fraction of the height of the tube is the height of the table?

is your sense of what numbers mean. Ex. 2×3=6

Taking large numbers and splitting them into small, manageable units.

Recall information, Skills and Concepts, Strategic Thinking and Extended Thinking.

refers to cognitive demand of tasks associated with a specific benchmark; can be low, mod, or high depend on what is req

Select the least appropriate manipulative for fraction concepts.

Concrete uses tiling, base ten blocks

Which of the following concepts is recommended to be taught 1 in development of fractional understanding for students

Assessment Choice: Oral report; Venn diagram; multiple methods; calendar math

________is a geometric visual that uses patterns with no gaps to assist a student in calculating a value, such as area.

4th grade teacher wanted to use an alternative assess method following her students' study of Seminoles in FL in 1700's

A first-grader explained the following to his teacher: "I know that 7+3=10. And I know all my doubles, so I know 5+5=10.

solve a mathematical problem using standard notation in:

A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

Key words: identify, recall, recognize, use, measure, facts, definitions, procedures, applying a formula.

_____in elemen math relate to the speed and _____ of which the student can answer a basic math fact. is a 4 step process

Deriving a mathematical model to make a prediction is which level of thinking of Webb's Depth of Knowledge?

shows that there is always another fraction to be found between any two numbers. The unit of distance or length.

Students are at a pictorial level in terms of development. What is an ex. of something students might be using in class

A ______________ is more student-directed

Compacting: Groups of students who can skip steps and move quickly because they have advanced math fluency.

_______________are methods in which students invent ways to solve complex problems.

Jon had two books. Kevin gave him 4 more books. How many books does Jon have now? 2 + 4 =?

Used to teach... Area and perimeter, fractions, transformations

Abstract just knowing the math problem. (2 x 5 is 10)

Four types of addition and subtraction problems: join, separate, part- part- whole, compare.

Petra has three fewer fish than Deana. Deana has eight fish. How many fish does Petra have? ?+3 = 8

Req student to make decision about how approach problem. Collect, classify, organize & Compare data in charts/ make obs.

If 18 apples are arranged into 3 equal rows, how many apples will be in each row?

A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

Used to teach...Place value, operations

Assessment Choice: Demonstrate using a model; matching solution procedures to written problems; paper-and-pencil

Borrowing pieces of one number to compensate for another to make it easier to solve.

Req reasoning, planning, thinking over an ext. period of time. High cog demand. Make prediction, connection, relate idea

Assessment Choice: Portfolio from an activity menu