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 (2006).
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 7 are shaded.)
Expectations
To monitor students' growth across and within grades, there are
a set of Expectations that describe 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 |
Represent and identify quantities using connecting links, coins, and symbols. |
| E2 |
Connect representations of quantities (e.g., ten frames, connecting links, coins, symbols). |
| E3 |
Skip count by fives and tens and count on to find the value of a set of coins. |
| E4* |
Group and count objects by twos, fives, and tens and count on to count the leftovers. |
| E5 |
Compare and order quantities (e.g., lengths using comparative language: shorter, longer,
shortest, longest). |
| E6 |
Solve addition problems involving length and whole numbers whose sums are less than 30 using tools (e.g., connecting links, tables, graphs). |
| E7 |
Recognize that the measure of a length is dependent on the size of the unit of measure (e.g., a pencil is 4 large paper clips or
6 small paper clips). |
| E8 |
Connect activities and events to the passage of time using actions, drawings, and stories. |
| E9* |
Measure and estimate length using nonstandard units (e.g., paper clips) and standard units (e.g., inches). |
| E10 |
Make a bar graph to find information about a data set. |
| E11 |
Read a table or bar graph to find information about a data set. |
| E12 |
Use mental math strategies to add (direct modeling, counting strategies, reasoning from known facts) for the facts in Group C with sums to ten. |
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 |
| E3. |
Skip count by fives and tens and count on to find the value of a set of coins. |
|
| E4.* |
Group and count objects by twos, fives, and tens and count on to count the leftovers. |
|
| E8. |
Connect activities and events to the passage of time using actions, drawings, and stories. |
|
| E9.* |
Measure and estimate length using nonstandard units (e.g., paper clips) and standard units (e.g., inches). |
- Variations of measurement DPPs
Item K Find an Object: Links,
Item L Find Two Objects: Links,
Item W Find an Object: Inches,
Item X Find Two Objects: Inches,
and Item Y Measure with Two Units
|
| E12. |
Use mental math strategies to add (direct modeling, counting
strategies, reasoning from known facts) for the facts in Group C
with sums to ten. |
|
* Denotes Benchmark Expectation
Figure 3: Expectations for Unit 7 with opportunities
for targeted practice
Activities
There are three activities in this unit that can be modified to provide targeted practice. These activities can be placed in a learning center or used as part of class transitions or in another setting.
Games
There are three games that can be used to provide targeted practice. Games can be placed in a learning
center or used in another setting. Use the first two games to develop strategies for the addition facts in
Group C.
) on the Unit 7
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 and
receiving feedback.