Embedded Files
The math learning progressions below were downloaded from OGAP Math LLC. You can open and download the progression by clicking on the image. The student work examples that are used to illustrate how to use the progressions and interpret student work were taken from the accompanying OGAP books referenced below under "To go deeper" and published by Routledge as part of their Bringing Mathematics Education Research to the Classroom Series.
We suggest the following learning progressions by grade span, although looking across all progressions can help an educator better understand how students develop mathematical skills across the K-8 grade span:
K-2: Base Ten Number Progression | Addition & Subtraction Progression
Gr 3-4: Addition & Subtraction Progression | Multiplication & Division Progression | Fractions Progression
Gr 5-6: Multiplication & Division Progression | Fractions Progression | Ratio & Proportions Progression
Gr 7-8: Fractions Progression | Ratio & Proportions Progression
OGAP Base Ten Number Progression.pdfBASE TEN NUMBER PROGRESSION
BASE TEN NUMBER PROGRESSION
K-2: Slide deck with student work examples in a printable handout
Additive Framework Color.pdfaddition & Subtraction PROGRESSION
addition & Subtraction PROGRESSION
K-2 Addition: Slide deck with student work examples in a printable handout
K-2 Subtraction: Slide deck with student work examples in a printable handout
Gr 3-4 Addition: Slide deck with student work examples in a printable handout
To go deeper:
Ebby, C. B., Hulbert, E. T., & Broadhead, R. M. (2021). A Focus on Addition and Subtraction: Bringing Mathematics Education Research to the Classroom. Routledge.
OGAP-Multiplicative-Framework-Color-10.11.2022pdf (3).pdfMultiplication & Division PROGRESSION
Multiplication & Division PROGRESSION
Gr 3-4 Multiplication & Division: Slide deck with student work examples in a printable handout
Gr 5-6 Multiplication & Division: Slide deck with student work examples in a printable handout
To go deeper:
Hulbert, E., Petit, M. M., Ebby, C. B., Cunningham, E. P., & Laird, R. E. (2024). A Focus on Multiplication and Division: Bringing Mathematics Education Research to the Classroom (2nd ed.). Routledge.
OGAP Fraction-Framework-Color-6.2018.pdffractions PROGRESSION
fractions PROGRESSION
Gr 3-4 Fractions: Slide deck with student work examples in a printable handout
Gr 5-6 Fractions: Slide deck with student work examples in a printable handout
Gr 7-8 Fractions: Slide deck with student work examples in a printable handout
To go deeper:
Petit, M. M., Laird, R. E., Ebby, C. B., & Marsden, E. L. (2022). A Focus on Fractions: Bringing Mathematics Education Research to the Classroom (3rd ed.). Routledge.
OGAP_Proportion_Framework_12.11.2019_V2.pdfratio & proportions PROGRESSION
ratio & proportions PROGRESSION
Gr 5-6 Ratio & Proportions: Slide deck with student work examples in a printable handout
Gr 7-8 Ratio & Proportions: Slide deck with student work examples in a printable handout
To go deeper:
Petit, M. M., Laird, R. E., Wyneken, M. F., Huntoon, F. R., Abele-Austin, M. D., & Sequeira, J. D. (2020). A Focus on Ratios and Proportions: Bringing Mathematics Education Research to the Classroom. Routledge.
Learning progression videos
Learning progression videos
https://gfletchy.com/progression-videos/
These videos show how students develop mathematical skills by showing examples of increasingly more sophisticated thinking and how it connects to later mathematical reasoning.
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