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 5 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 |
Group and count objects by twos, fives, and tens. |
| E2* |
Skip count by fives and count on to find the value of a set of coins. |
| E3 |
Read and write numbers to 50. |
| E4 |
Represent and identify quantities using counters, coins, number lines, ten frames, 100 Chart,
pictures, data tables, and graphs.
|
| E5 |
Connect representations of quantities (e.g., number lines, coins, counters, pictures, symbols, ten
frames, data tables, graphs). |
| E6* |
Divide a collection of objects into groups of a given size including groups of ten and count
the leftovers. |
| E7 |
Solve addition word problems involving two or three whole numbers whose sum is less than 30
using tools (e.g., counters, diagrams, ten frames, data tables, bar graphs). |
| E8 |
Collect and organize information in a data table. |
| E9 |
Make a bar graph to find information about a data set. |
| E10 |
Read a data table or bar graph to find information about a data set. |
| E11 |
Make predictions and generalizations about a data set using a data table and bar graph. |
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. |
Group and count objects by two, fives, and tens. |
|
| E3. |
Read and write numbers to 50. |
|
| E4. |
Represent and identify numbers using counters, coins, number
lines, ten frames, 100 Chart, pictures, data, tables, and graphs. |
|
| E5. |
Connect representations of quantities (e.g., number lines,
coins, counters, pictures, symbols, ten frames, data tables,
graphs).
|
|
| E6. |
Divide a collection of objects into groups of a given size
including groups of tens and count the leftovers.
|
|
|
Figure 3: Expectations for Unit 5 with opportunities for targeted practice
Activities
There are several activities in this unit that can also be a vehicle for providing targeted practice.
Once introduced in the unit, these activities can be tailored to meet the needs of students. These activities can
be placed in centers or used in other settings or at home.
) on the Unit 5 Key Assessment Opportunities Chart. See Figure 2. In this unit, students will also get better acquainted with the Math Practices Expectations by discussing them in the context of a specific problem, receiving feedback, reviewing a peer's work, and revising their own work.