This tool gives an overview of the priority standards for grade 3. It connects the Drivers of Investigation to both the big ideas and the standards for mathematical practice (SMP). Periodically and throughout the school year, teachers can use a tool like this to assess and give feedback to students around their strengths and areas for growth. The teacher notes those indicators that the student has shown mastery, and which ones the student should focus on to further student learning. The final two columns are meant to be filled in by the teacher.
Considerations for the final two columns to be completed by the teacher (TBT):
Student Strength: What does the student understand in terms of this standard? What linguistic and cultural assets possessed by the students can I tap into to support all students, including those on the road to English proficiency, in their mastery of the content?
Student Area for Growth: What should the student focus on to strengthen their understanding of this standard?
| Content Connections | Big ideas | Mathematical Practice Standards | Indicators: The student… | Student Strength | Student Area for Growth |
|---|---|---|---|---|---|
| Communicating Stories with Data | Represent Multivariate Data | SMP1: Make sense of problems and persevere in solving them. SMP4: Model with mathematics SMP6: Attend to precision | -Interprets appropriate meaning from graphs -Strategically organizes multivariable data -Creates graphs that clearly communicate information from data | TBT | TBT |
| Communicating Stories with Data | Fractions of Shape and Time | SMP4: Model with mathematics SMP5: Use appropriate tools strategically. SMP6: Attend to precision | -Creates data visualizations that clearly capture and communicate about data collected over time | TBT | TBT |
| Exploring Changing Quantities | Addition and Subtraction problems | SMP3: Construct viable arguments and critique the reasoning of others. SMP5: Use appropriate tools strategically. SMP7: Look for and make use of structure. | -Computes sums and differences within 1000 -Justifies solutions using appropriate tools or models -Constructs arguments with clear reasoning to support solutions | TBT | TBT |
| Exploring Changing Quantities | Number Flexibility to 100 | SMP3: Construct viable arguments and critique the reasoning of others. SMP4: Model with mathematics. SMP5: Use appropriate tools strategically. | -Computes products and quotients within 100 -Justifies solutions using appropriate tools or models -Constructs arguments with clear reasoning to support solutions | TBT | TBT |
| Taking Wholes Apart, Putting Parts Together | Square Tiles | SMP2: Reason abstractly and quantitatively. SMP5: Use appropriate tools strategically. | -Measures area using square tiles as tools -Connects the area of individual square tiles to area of entire shape’s area using fractions. | TBT | TBT |
| Taking Wholes Apart, Putting Parts Together | Fractions of shape and time | SMP2: Reason abstractly and quantitatively. SMP4: Model with mathematics SMP7: Look for and make use of structure | -Collects and organizes multivariable data in relationship to time -Creates connections that highlight the relationship between measures of time including minutes, quarter, and half hours. | TBT | TBT |
| Taking Wholes Apart, Putting Parts Together | Fractions as relationships | SMP2: Reason abstractly and quantitatively. SMP7: Look for and make use of structure | -Interprets the relationship between the numerator and denominator of fractions– especially in context -Recognizes and connects equivalent fractions to one another. | TBT | TBT |
| Taking Wholes Apart, Putting Parts Together | Unit Fraction Models | SMP3: Construct viable arguments and critique the reasoning of others. SMP4: Model with mathematics | -Uses visual models to compare unit fractions -Justifies arguments about unit fractions using visual models | TBT | TBT |
| Discovering Shape and Space | Analyze Quadrilaterals | SMP2: Reason abstractly and quantitatively. SMP4: Model with mathematics | -Compares quadrilaterals based on various features -Investigates how area and perimeter change when side lengths change. -Solves real world problems involving area and perimeter of quadrilaterals through modeling. | TBT | TBT |
| Discovering Shape and Space | Fractions as Relationships | SMP2: Reason abstractly and quantitatively. SMP4: Model with mathematics | -Creates visual representations that model fractions -Justifies how a model represents a fractional quantity by relating the numerator, denominator and visual. | TBT | TBT |
| Discovering Shape and Space | Unit Fraction Models | SMP3: Construct viable arguments and critique the reasoning of others. SMP4: Model with mathematics | -Uses visual models to compare unit fractions by attending to differences in scale -Justifies arguments about unit fractions using visual models | TBT | TBT |
Example Rubric based around YouCubed’s Halving task.
- This investigation gives opportunity for students to: Make sense of the world, using content from Taking Wholes Apart, Putting Parts Together, and Discovering Shape and Space and related standards of mathematical practice.
- The rubric is meant to encourage reflection and metacognition in students by providing space for them to show evidence of understanding and also pinpoint areas where they can still grow. Teachers use this rubric as a tool for formative assessment and feedback.
- Columns to be completed by teacher (TBT); Columns to be completed by student (TBS)
| Teacher feedback for area of growth: To keep growing, focus on… | Student reflection for area to grow: A question I have or something I still need to work on is… | Big Idea | Student reflection for material learned: I can show that I understand by… | Teacher feedback: A strength you have shown is… |
|---|---|---|---|---|
| TBT | TBS | Fractions as relationships: I understand that a fraction is a relationship between numerators and denominators – and I connect this understanding to the visuals in this task. (NF.1, NF.3 a,b, MP2 MP7) | TBS | TBT |
| TBT | TBS | Unit Fraction Models: I can compare unit fraction using different visual models. (NF.2, MP4, MP5) | TBS | TBT |
| TBT | TBS | I can justify my comparisons to convince myself and others. (NF.3d, MP1, MP3) | TBS | TBT |
| TBT | TBS | Analyze Quadrilaterals: I can describe, analyze, and compare quadrilaterals (4-sided shapes) and the ways the area changes when it is cut in different ways. (MD.8, G.1, G.2. MP2, MP4) | TBS | TBT |
| TBT | TBS | Square Tiles: I can think about fractions with shape and space, expressing the base unit as a unit fraction of the whole. (NF.1, G.2) | TBS | TBT |
California Department of Education, August 2021