Assessment in this unit
Key Ideas, Expectations, and Opportunities
Using Assessment to Meet Individual Needs
The explicit Expectations and assessment tasks in this unit describe what it means to "get it." Providing feedback
on these Expectations helps identify students who need to access the content another way, need further
practice opportunities, or are ready to extend or deepen their understanding of a concept. Instructional opportunities
that help support the varied needs of students also need to be identified. These opportunities provide
models that can be replicated or used multiple times and can be used in a variety of settings (e.g., home, transitions,
support classroom, as a center).
The Assessment Program serves the
following purposes:
- It provides information to teachers about what students know and can do. This information is used to guide instruction. An activity may help teachers answer questions about whole-class instruction: What do I do next? In the next minute? Next lesson? Next class? Next unit? Other assessments may help teachers decide how to support individual students, including those who struggle with a concept and those who are ready to be challenged.
- It communicates the goals of instruction to parents and students. What teachers choose to assess communicates to the class what they value. For example, if teachers want students to work hard at communicating problem-solving strategies, then it is important to assess mathematical communication.
- It provides feedback to students and parents about student progress. This includes teacher evaluation of student progress as well as students' assessment of their own progress.
Key Mathematical Ideas
The mathematical content in Math Trailblazers is organized around a set of Key Ideas. These Key Ideas are
based on the National Council of Teachers of Mathematics (NCTM) Standards for the grade band as well as
current thinking in the mathematics education community, e.g., Charles (2005), NCTM (2000), Van de Walle
(2005). There is a set of Key Ideas for each content strand: Number, Algebra, Geometry, Measurement, and
Data. They are based on "big ideas" in mathematics and describe what students should be able to do within
each strand. The Key Ideas are shown in the table in Figure 1.
1. Number Sense: Understand the base-ten number system, recognize relationships among quantities and numbers, and represent numbers in multiple ways. |
2. Operations: Understand the meaning of numerical operations and their application for solving problems. |
3. Computation and Estimation: Use efficient and flexible procedures to compute accurately and make reasonable estimates. |
|
1. Identifying Patterns: Identify and describe patterns and relationships, including how a change in one variable relates to a change in a second variable. |
2. Tables and Graphs: Represent patterns and relationships with graphs, tables, and diagrams. |
3. Symbols: Represent patterns and relationships with symbols (includes using variables in formulas and as unknowns in equations). |
4. Using Patterns: Apply relationships, properties, and patterns to solve problems, develop generalizations, or make predictions. |
1. Shapes: Identify, describe, classify, and analyze 2- and 3-dimensional shapes based on their properties. |
2. Orientation and Location: Use coordinate systems to specify locations and describe spatial relationships. |
3. Motion: Apply transformations (slides, flips, and turns) and use symmetry to analyze mathematical situations. |
4. Geometric Reasoning: Use visualization, spatial reasoning, and geometric modeling to solve problems. |
1. Measurement Concepts: Understand measurable attributes of objects or situations (length, area, mass, volume, size, time) and the units, systems, and processes of measurement. |
2. Measurement Skills: Use measurement tools, appropriate techniques, and formulas to determine measurements. |
1. Data Collection: Select, collect, and organize data to answer questions, solve problems, and make predictions. |
2. Data Representation: Select and create appropriate representations, including tables and graphs, for organizing, displaying, and analyzing data. |
3. Data Description: Describe a data set by interpreting graphs, identifying patterns, and using statistical measures, e.g., average and range. |
4. Using Data: Apply relationships and patterns in data to solve problems, develop generalizations, and make predictions. |
Figure 1: Key Ideas for Math Trailblazers (Key Ideas addressed in Unit 13 are shaded.)
Expectations
To monitor students' growth across and within grades, there is a set of Expectations that describes what
students are "expected" to do within each content strand. Expectations show the growth of the mathematical
content within the Key Ideas for each strand.
EXPECTATIONS |
|
Use this list of Expectations to assess students on the key concepts and skills in this unit. |
E1* |
Identify, describe, sort, and draw 2-dimensional shapes based on their attributes (e.g., square
corners, number of sides, number of angles, number of parallel sides). |
E2* |
Partition shapes and sets into equal shares. |
E3 |
Partition a rectangle into rows and columns of the same size unit to find the area. |
E4* |
Use words and models to describe equal shares (e.g., half, half of). |
E5 |
Recognize that equal shares of the same whole do not have to be the same shape. |
E6 |
Compose and decompose shapes into smaller shapes. |
E7* |
Recognize that the same fractional parts of different-size unit wholes are not equal. |
E8* |
Find the area of a shape on a grid using counting, repeated addition, and reasoning strategies. |
E9 |
Recognize that different shapes can have the same area. |
E10* |
Demonstrate fluency with the subtraction facts related to the addition facts in Group E
(11 − 1, 11 − 10, 12 − 2, 12 − 3, 12 − 4, 12 − 5, 12 − 7, 12 − 8, 12 − 9, 12 − 10,
13 − 3, 13 − 4, 13 − 5, 13 − 8, 13 − 9, 13 − 10, 14 − 5, 14 − 9). |
E11 |
Determine the unknown number in an addition or subtraction sentence relating three whole
numbers for the facts in Group E. |
Targeted Practice
This unit provides opportunities for additional targeted practice for some of the
Expectations. See the chart in Figure 3 and the descriptions that follow. These opportunities connect directly
to assessment tasks, so the practice can be tailored to the current level of student progress.
- For students who are struggling with the Expectation, practice is targeted toward the foundational concepts
and skills involved and often provides a different way to access the content.
- For students who are making significant progress toward the Expectation, practice is designed to help
move toward proficiency and autonomy.
- For students who are already meeting the Expectation, opportunities are provided to deepen or extend
understanding.
Expectation |
Opportunities for Targeted Practice |
E1.* |
Identify, describe, sort, and draw
2-dimensional shapes based on their attributes
(e.g., square corners, number of sides, number
of angles, number of parallel sides). |
|
E2.* |
Partition shapes and sets into equal shares. |
|
E4.* |
Use words and models to describe equal
shares (e.g., half, half of). |
|
E6. |
Compose and decompose shapes into
smaller shapes. |
|
E7.* |
Recognize that the same fractional parts of
different-size unit wholes are not equal. |
|
E8.* |
Find the area of a shape on a grid using
counting, repeated addition, and reasoning
strategies. |
|
E9.* |
Recognize that different shapes can have
the same area. |
|
* Denotes Benchmark Expectation
Figure 3: Expectations for Unit 13 with opportunities for targeted practice
Activities
There are several activities described in this unit that can be used to provide targeted practice.
These activities can be tailored to meet the needs of students. The activities can be placed in a learning center,
sent home, or used in other settings.