Screeners
As the intervention framework suggests, the beginning spot is to give general screeners to all students in the class. The suggested screeners (below) ask students to recall/use content from previous grade levels. Teachers may choose to only use parts of the screeners that are applicable to the unit/content they intend to teach. This will give a baseline for the class to help the teacher determine what topics are well-learned, what topics the whole class needs support in, and what topics would be best for small groups or individuals.
The suggested screeners are from the Sask Math site and can be found here.
Intervention Sheets
Once screeners evidence is gathered, the intervention sheets will be valuable. Intervention sheets are found either by navigating through the "Organized by Skill" or "Organized by Grade" pages on this website. Each intervention sheet includes:
An outcome for a specific grade
Deeper Diagnostic tool suggestion(s)
Concrete-Representational-Abstract (CRA) Continuum Progression links for that grade level
Suggestions for CRA Tools and Representations to use with that grade level and concept
A list of possible Low Floor/High Ceiling Tasks
Places where teachers can turn to find Fluency Practice Activities to use with that grade level and concept
Read below for an explanation of each of these elements, and others that will be useful when planning intervention sessions.
Deeper Diagnostics
After gathering screener data, the next step in the PSSD Intervention Framework is to do a deeper diagnostic in order to gather skill-specific areas where intervention is necessary. The following are resources that can be used to do a deeper diagnostic.
Building Computational Fluencies
This is an American Resource. Some of the resource uses American money. The resource is available online and has been linked to the main working document.
The diagnostic assessments may have more extensive than you need for a specific outcome. Choose pages and questions appropriately. Each assessment suggests different activities to support intervention. Choose one that are appropriate to the student.
Each grade of the workbook goes back to basics starting at basic facts. So, if you see Building Computational Fluency Grade 3 in the grade 1 outcomes this is why. This could be helpful in choosing assessments or choosing assessments for older students who require intervention for basic facts.
Gap Closing
This free resource comes from Ontario and was written by Marian Small. The resource is available online and has been linked to the main working document.
The diagnostic assessments may have more extensive than you need for a specific outcome. Choose pages and questions appropriately. Each book is broken down into smaller parts. Each book, as a whole, may not be appropriate for each student or grade level. Choose the sections as needed. The Facilitators Guide explains how to use information from the diagnostic to choose the intervention material.
Each book and section contains a “Think Sheet” to help explain the information and gives examples. Note: Fluency Practice is to be worked after mini lesson or other practice.
Leaps and Bounds
Leaps and Bounds is an intervention program by Marian Small. Each grade level included intervention for the grade outcomes below, no new grade level material is introduced.
Each diagnostic will help you determine which pathway to take after assessment. Each Topic pathway has worksheet materials that can be used for practice.
This program is for purchase from Nelson at the following link.
CRA Progression
CRA or Concrete, Representational, Abstract progression, isn’t just a linear progression like climbing a staircase. It’s more like a dynamic framework where students move fluidly between the concrete, representational, and abstract stages, making connections and building understanding along the way.
What is CRA?
Concrete (C): Hands-On Learning
In the concrete stage, students engage in hands-on learning experiences using physical manipulatives. Picture students using base 10 blocks and a Place Value Chart to represent the number 126 or arranging bundled craft sticks to understand addition and subtraction. This tactile approach helps students develop a solid grasp of mathematical concepts by connecting abstract ideas to real-world experiences.
Representational (R): Visual Representations
Moving on to the representational stage, students transition from physical manipulatives to visual representations. Here, they use drawings, diagrams, or other visual aids to represent or replace physical objects. For example, students might draw a base ten drawing of 126 to represent the quantity they previously counted with sticks. (Using a square to represent hundreds, tally marks for tens, and dots arranged in a dice pattern for ones.) Visual representations provide a bridge between concrete experiences and abstract concepts, helping students visualize mathematical relationships.
Abstract (A): Symbolic Representation
Finally, in the abstract stage, students work with numbers and symbols to represent mathematical concepts. This is where they understand that numbers and symbols can stand in for the concrete objects and visual representations they’ve encountered earlier. For instance, students recognize that the numerals 1, 2, and 6 in the number 126 represent a value of 1 hundred, 2 tens, and 6 ones. The abstract stage solidifies students’ understanding of mathematical concepts and prepares them for more complex problem-solving tasks.
The abstract stage includes standard algorithms, which are needed for efficiency and accuracy since drawing or building math problems every time would become time-consuming and error-prone. Our curriculum describes these stages as concrete, pictorial, and symbolic.
Here is a blog post from Shelley Gray that describes this CRA progression with some diagrams to support.
This post from Mathematics Hub also has some detail for both elementary and upper years classrooms on using the CRA framework.
Additionally, using virtual manipulatives (like Polypad) is also effective when you don’t have access to concrete materials. Especially as students age, or as the concepts become more complex, using virtual manipulatives means the framework is VRA instead of CRA and is still helpful to develop and deepen understanding.
For a list of some peer-reviewed articles on this framework, you can start here as some articles are public access ERIC list of articles. One meta-analysis of multiple studies on the use of CRA includes the following statement, “These data suggest that CRA is an effective intervention for increasing math skills across varying operations, types of intervention, grades, and students with and without disabilities” (Ebner, MacDonald, Grekov, & Aspiranti, 2025, p. 38).
Saskatchewan-specific support for CRA can be found through The Numeracy Project. This is a learning resources created for the Ministry of Education Numeracy Project and includes:
a document that identifies a big idea in a curricular outcome, questions for classroom instruction for student assessment, sample answers shown concretely, pictorially and symbolically and connecting outcomes;
reference documents that provide further information or resources;
additional questions across multiple grades for each big idea found in a progression document; and,
short videos.
The numeracy project is a curriculum, instruction and assessment support for mathematics. The learning supports are aligned directly to Saskatchewan curricular outcomes.
Low Floor/High Ceiling Tasks (Teacher Directed Activities)
These tasks are structured in such a way that all learners, regardless of their mathematical understanding, can enter the conversation. These types of questions have a low floor (learners do not require a deep understanding to contribute to the conversation) and a high ceiling (learners with a more advanced understanding can be pushed to extend their understanding). Examples of these questions can be found through the following sources:
The name “Open Middle” might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:
a “closed beginning” meaning that they all start with the same initial problem.
a “closed end” meaning that they all end with the same answer(s).
an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.
Open Middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards from the States, align with many of our Saskatchewan’s curricular outcomes, and provide students with opportunities for discussing their thinking.
Some additional characteristics of Open Middle problems include:
They generally have multiple ways of solving them as opposed to a problem where you are told to solve it using a specific method.
They may involve optimization such that it is easy to get an answer but more challenging to get the best or optimal answer.
They may appear to be simple and procedural in nature but turn out to be more challenging and complex when you start to solve it.
They are generally not as complex as a performance task which may require significant background context to complete.
Open Middle problems might have a few different versions. Use these to change the level of the floor or ceiling. Have students determine the easiest answer and then add on other guidelines.
Amplify Classroom is a free teaching and learning platform that places student engagement at the center of instruction.
Amplify Classroom features free lessons, lesson-building tools, sharing features, and more. Built by math educators, the platform makes leaning into good pedagogy easier for teachers—which makes the lesson a more interactive experience for students. Desmos has both a graphing calculator and some other activities (some built by Amplify teachers and others searchable on the internet) that are also accessible for free. Some Amplify lessons require a paid subscription, but the graphing calculator will always remain free.
This website has numerous high floor low ceiling math tasks sorted by Saskatchewan Curriculum outcome. They are curated by Kyle Webb and Maegan Giroux, co-authors of the most recent Building Thinking Classrooms books.
Number Talks
Number Talk are conversations with students that pulls out their thinking for all to see. Examples can be found
Sherry Parrish Books
Fluency Practice Activities (Partner Practice of More Independent)
These activities are opportunities to solidify students retrieval of math facts they have previously learned.
Cover Copy Compare is a low stakes way for students to practice Math Facts. You can either write a list of facts with answers on the board for students to copy or type into an editable PDF and print. Students fold along the line to cover the math facts. Students then read one fact at a time, cover the fact with the folded paper, copy the fact in the empty space, then compare their copy with the original. If they are incorrect they do it again. This helps create strong neural pathways that are connecting the correct answer with the math fact with immediate feedback.
That One
This routine uses teacher created examples of grade level appropriate short expressions. For example, for different grade levels you might choose one of these, and supplement with similar expressions: 99 + 14, 0.25 x 48, 7 ÷ 1/3. Students are asked to determine which ones are best suited to being solved by the algorithm, and which ones are best solved by a reasoning strategy. It is important to have students explain their decisions for their determination.