Knowledge of Student Thinking and Instructional Practices
change unknown
A + ___ = C
Diagnostic
A pre-assessment providing instructors with information about students' prior knowledge, preconceptions, and misconceptions before beginning a learning activity.
Formative Assessment
A range of formal and informal assessments or checks conducted by the teacher before, during, and after the learning process in order to modify instruction.
Number of groups unknown
A red hat costs $18, and a blue hat cost $6. How many times as much of the blue hat does the red hat cost? ? x 6 = 18 and 18 / 6 =?
Group size unknown Word Problem
A red hat costs $18, and that is 3 times as much as the cost of a blue hat. How much does a blue hat cost? 3 x ? = 18 and 18 / 3 =?
Criterion-Referenced Assessment
An assessment that measures student performance against a fixed set of predetermined criteria or learning standards.
Geoboard
Area Perimeter Properties of Basic Shapes Congruency and Similarity
Area: Unknown Product
Area Example: What is the area of a 4cm by 5cm rectangle? 4 x 5 = ?
Arrays: Unknown product
Array Example
Diagnostic example
Before starting a unit on quadrilaterals, a teacher gives a quick assessment to determine students knowledge, understanding, and barriers regarding geometry.
Compensation
Borrowing pieces of one number to compensate for another to make it easier to solve. Compensation 46 + 38 = Take 4 from 38 and give it 46. 50 + 34 = 84
Snap cubes
Combine like terms Represent ratios Distributive property Multiply polynomials Factoring polynomials
Compare (Multiplication and Division)
Compare problems occur first with whole numbers (two times as much) and then phase it unit fractions (one-half as much) in the fifth grade. Either grade level scenario is possibly on the test.
Equal Groups: Number of Groups Unknown
How many groups? Division
Group size unknown
How many in each group? Division
Unknown Product
Multiplication
Fraction Strips
Perform operations with Fractions Represent Fractional Parts
tiles
Perform operations with Fractions Represent Fractional Parts
base ten blocks
Place value Whole number operations Comparing numbers Regrouping with addition and subtraction Area and Volume
Counters
Sorting Counting
Attribute blocks is a type of manipulative most effectively used to teach which of the following sets of concepts?
Sorting Patterns Attributes of figures
Transitivity
The transitivity principle states that if A is related to B and B is related to C in the same way, then A is also related to C.
unknown product
Word Problem A blue hat cost $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost? 6 x 3 = ?
tiling
a geometric visual that uses patterns with no gaps to assist a student in calculating a value, such as an area. The area of the shape that follows is 15 units.
Add to: Result Unknown
a number given, and more is being added to the number to find a sum
Take From: Result Unknown
a number is given, and some is being taken from this number to find the difference.
Subitize
a student's ability to quickly identify a number of items in a small group without having to count them regardless of the arrangement of items.
Performance-based assessment example
after reading text about parallelograms, students create kites by measuring the dimensions and angles of the kite materials.
Norm reference (percentile)
an assessment or evaluation that yields an estimate of the position of the tested individual in a predefined dual in a p
Summative
an assessment that focuses on the outcomes. It is frequently used to measure the effectiveness of a program, lesson, or strategy.
Performance-based assessment
an assessment that measures student's ability to apply the skills and knowledge learned from a unit or units study; the task challenges students to use their higher-order, critical thinking skills to create a product or complete a process.
Standard Algorithm
is a specific method of computation which is conventionally taught for solving particular mathematical problem using standard notation in: Exchanging Regrouping Long division Long multiplication Average Area Volume.
inventive strategies
methods in which students invent ways to solve complex problems. They involve using reason and understand to get to an end result. ex. partitioning, compensation
Iteration
repeated interactions with the same partners Listing multiples by adding the same number to the number before each time is an example of iteration. Multiples of 3: 3 3 + 3= 6 6 + 3= 9 9 + 3 =12 12 + 3= 15
bar diagram
solve for unknown value using one of the four operations & solve word problems (whole, part, part)
Partitioning
taking large numbers and splitting them into small, manageable units Partitioning 467 - 122 = 400 - 100= 300 60 - 20 = 40 7 - 2 = 5 345
Put Together/Take Apart, Total Unknown
this is often referred to as PART-PART-WHOLE. Part of the number is given, then another part is given to make a total amount.
addend unknown (put together/take apart)
this is often referred to as PART-PART-WHOLE. Part of the number is given, then another part is given to make a total amount.
Smaller Unknown, Compare
two value are given for a total, with the size of one being compared to the size of the other. "Fewer" Version
Difference Unknown
two value are given for a total, with the size of one being compared to the size of the other. "How many more?"
Bigger Unknown, Compare
two value are given for a total, with the size of one being compared to the size of the other. "More" Version