MTTC Subarea Two PP

Attribute of a shape

A characteristic or property of a geometric figure, such as its sides, angles, vertices, or size.

Defining attributes

Characteristics that determine what a shape is (for example, a triangle having $3$ straight sides).

Nondefining attributes

Characteristics that do not determine a shape's identity, such as color, size, or orientation.

Purpose of identifying defining attributes

To understand why a shape belongs to a particular category rather than identifying it only by appearance.

Vertex

A point where two or more line segments or edges meet.

Angle

A figure formed by two rays or line segments that share a common endpoint.

Two-dimensional (2D) shape

A flat shape that has length and width.

Three-dimensional (3D) shape

A solid shape that has length, width, and height.

Regular polygon

A polygon with all sides equal in length and all angles equal.

Irregular polygon

A polygon whose sides or angles are not all equal.

Polygon

A closed, two-dimensional shape made of straight line segments.

Number of sides in a triangle

$3$ sides.

Number of sides in a quadrilateral

$4$ sides.

Rectangle

A quadrilateral with $4$ right angles and opposite sides equal in length.

Square

A quadrilateral with $4$ equal sides and $4$ right angles.

Parallelogram

A quadrilateral with $2$ pairs of parallel opposite sides.

Rhombus

A quadrilateral with $4$ equal sides.

Trapezoid

A quadrilateral with at least $1$ pair of parallel sides.

Face (3D shape)

A flat surface on a three-dimensional object.

Edge (3D shape)

A line segment where two faces meet.

Vertex (3D shape)

A corner point where edges meet.

Cube

A three-dimensional shape with $6$ square faces.

Rectangular prism

A three-dimensional shape with $6$ rectangular faces.

Sphere

A round three-dimensional shape with $1$ continuous curved surface and no edges or vertices.

Cone

A three-dimensional shape with $1$ circular base and $1$ curved surface that comes to a point.

Cylinder

A three-dimensional shape with $2$ circular bases and $1$ curved surface.

Composite shape

A figure made by combining two or more simpler shapes.

Net of a 3D shape

A flat, two-dimensional arrangement that can be folded to form a three-dimensional shape.

Transformation (geometry)

A movement or change in the position or size of a shape.

Translation (geometry)

Sliding a shape from one position to another without turning or flipping it.

Rotation (geometry)

Turning a shape around a fixed point.

Reflection (geometry)

Flipping a shape over a line to create a mirror image.

Dilation (geometry)

Changing the size of a shape while maintaining its proportions.

One-to-one correspondence

Matching $1$ number word to exactly $1$ object when counting.

Cardinality

Understanding that the last number counted represents the total number of objects in a group.

Subitizing

Recognizing the number of objects in a small group without counting each one individually.

Perceptual subitizing

Recognizing the number of objects in a group immediately, without using smaller groups.

Conceptual subitizing

Seeing a group as smaller groups and combining them to recognize the total.

Hierarchical inclusion

Understanding that each number includes all the numbers before it (for example, $5$ includes $4$ and $1$).

Conservation of number

Understanding that the quantity of a group stays the same even when the objects are rearranged.

Counting all

Counting every object in a group from $1$ to determine the total.

Counting on

Starting with a known quantity and counting forward to find the total.

Counting back

Starting with a number and counting backward to subtract or find how many remain.

Efficiency of counting on compared to counting all

Students do not need to recount the entire group; they begin with a known quantity.

Composing numbers

Combining smaller numbers to make a larger number.

Decomposing numbers

Breaking a number into smaller parts.

Number bonds

Visual models that show how a number can be separated into two or more parts.

Significance of 5 and 10 as anchor numbers

They help students recognize quantities and develop efficient strategies for adding and subtracting.

Role of a five-frame in number sense

Helps students visualize quantities up to $5$ and recognize combinations that make $5$.

Role of a ten-frame in number sense

Helps students visualize numbers to $10$ and understand combinations that make $10$.

Ten-frame

A visual model with $2$ rows of $5$ spaces used to represent numbers up to $10$.

"Make a ten" strategy

Combining numbers to create a group of $10$, often to make addition easier.

Number line

A visual representation of numbers in order that can show counting, addition, and subtraction.

Open number line usage

Making jumps forward or backward along an unmarked line to represent addition and subtraction strategies.

Hundred chart

A chart displaying numbers from $1$ to $100$ in rows of $10$.

Role of a hundred chart in understanding number patterns

Enables students to identify counting patterns, skip counting, and relationships between numbers.

Place value

The value of a digit based on its position in a number.

Value of the 3 in 345

$300$, because the $3$ is in the hundreds place.

Value of the 4 in 345

$40$, because the $4$ is in the tens place.

Value of the 5 in 345

$5$, because the $5$ is in the ones place.

Base-ten system

Our number system organized around groups of $10$.

Number of ones that make one ten

$10$ ones.

Number of tens that make one hundred

$10$ tens.

Decomposition of 345 using place value

$3$ hundreds, $4$ tens, and $5$ ones.

Expanded form of 345

$$300 + 40 + 5$$

Regrouping 34 ones

$3$ tens and $4$ ones.

Concrete mathematical representation

Using physical objects or manipulatives to represent mathematical ideas.

Pictorial mathematical representation

Using drawings, pictures, or diagrams to represent mathematical ideas.

Abstract mathematical representation

Using numbers, symbols, and equations to represent mathematical ideas.

Concrete-representational-abstract (CRA) approach

Teaching a concept through hands-on objects, then drawings, and finally numbers and symbols.

Purpose of multiple mathematical representations

Helps students develop a deeper understanding by seeing the same mathematical idea in different ways.

Manipulatives

Physical objects students use to explore and represent mathematical concepts.

Base-ten blocks

Manipulatives representing ones, tens, hundreds, and thousands.

Unit cube (base-ten blocks)

Represents $1$.

Rod (base-ten blocks)

Represents $10$.

Flat (base-ten blocks)

Represents $100$.

Array

An arrangement of objects in equal rows and columns.

Role of an array in number understanding

Helps students visualize equal groups, repeated addition, and multiplication.

Equivalent representation

Different models or expressions that represent the same mathematical value.

Importance of students explaining their strategies

Helps teachers understand students' mathematical thinking and identify misunderstandings.

Number talk

A short classroom discussion in which students mentally solve a problem and explain their strategies.

Teacher's role during a number talk

Encourage different strategies, ask students to explain their reasoning, and compare approaches.

Open-ended mathematical question

A question that allows multiple strategies or possible answers.

Purpose of asking students how they got an answer

To understand their reasoning rather than focusing only on whether the answer is correct.

Error analysis

Examining a student's incorrect answer or strategy to identify the misunderstanding.

Teacher action when a student makes a mathematical error

Ask questions to uncover the student's thinking and provide support that addresses the misunderstanding.

Formative assessment

Assessment during instruction that helps teachers monitor learning and adjust teaching.

Diagnostic assessment

An assessment used to identify a student's strengths, weaknesses, and specific learning needs.

Observation assessment

Watching and listening to students as they work to gather information about their mathematical understanding.

Rationale for multiple assessment methods

Provides a more complete picture of student understanding.

Eliciting mathematical thinking

Asking questions or providing tasks that reveal how students understand and approach a problem.

Interpreting mathematical thinking

Analyzing a student's explanation, strategy, or work to understand their reasoning.

Supporting mathematical thinking

Providing guidance, questions, and representations that help students develop understanding.

Extending mathematical thinking

Challenging students to build on what they already understand and explore more complex ideas.

Productive mathematical question

A question that encourages students to explain, reason, compare, or justify their thinking.

Reason to avoid immediately telling the correct answer

Students need opportunities to reason, discover relationships, and develop their own understanding.

Regrouping in base-ten mathematics

Exchanging units of one place value for an equivalent amount in another place, such as $10$ ones for $1$ ten.

Different ways to represent 24

$2$ tens and $4$ ones; $1$ ten and $14$ ones; or $24$ individual ones.

Purpose of trading with base-ten blocks

To help students understand that different groups of units can represent the same quantity.