The following are a collection of resources to support educators in planning and designing for mathematics and numeracy grounded in the BC K-7 mathematics curriculum. Many of these ideas can also apply to grades 8-12 contexts.
BEGINNING OF THE SCHOOL YEAR
As you begin planning for the school year, consider thinking about the story of math is for the grade/s you will be teaching. What are new and foundational concepts? How will your students experience mathematics and develop curricular competencies? What openings are you creating for all students to engage in mathematics? What opportunities might students have to apply mathematics to other areas of learning or contexts? What materials will support student thinking? and maybe most importantly, What math story will your students leave the school year with? What will they have learned? How will they feel about math? How will their understanding of what mathematics is have been broadened and deepened? What will their math identity be?
The focus of the beginning of the school year is to set the tone for mathematics learning, build discourse and community and focus on a culture of learning. You may begin the year inviting students to engage in collaborative math tasks or problem-solving. There are many resources available for tasks and problems such as those from Dr. Marian Small’s Open Questions, Dr. Peter Liljedahl HERE or YouCubed HERE and HERE.
Routines and collaborative tasks set the tone for how mathematics will be experienced. Consider beginning the year with accessible routines such as Dot Images/Number Talk Images to help build norms around taking risks, being flexible with thinking, visualizing, explaining thinking and listening to others’ ideas. Engaging in this type of routine also helps to highlight the idea that there isn’t only one way or a right way to do math.
You could also begin the school year with a focus on big questions such as:
- What is math?
- Who does math?
- Where, when and how do we do math?
- Why is math important?
Exploring questions like the above give you a sense of what students know and feel about mathematics as well as what assumptions they might already have about what math is. This is an opportunity to discuss how math is used and enjoyed in different contexts such as at home, outdoors, or during sports for example. Students’ math identities are also very much connected to their family and cultural identities and creating openings for students to share a range of strategies they know, language, or games that are important to them helps to welcome all children to mathematics. Sharing biographies and some of the work of mathematicians from diverse cultures and backgrounds also helps to inspire and connect students to mathematics. A book list of suggested biographies can be found HERE.
Public schools in the Seattle area begin their school year with doing Counting Collections in K-5 classrooms. It is collaborative, accessible, social, and grounded in CGI research. Observing and listening to students doing counting collections provides information not just on counting but what students know about equal grouping, counting on, counting by multiples, place value, and representing numbers in concrete, pictorial and symbolic forms. This is the “assessment” that is used at the beginning of the year to see where student are in their learning.
If you are required to do some sort of more formal assessment of students at the beginning of the year, the Island Numeracy Network has BC curriculum-aligned tools for grades 3 and up HERE. In Richmond, we have the K-2 Numeracy Assessment Tool HERE and a draft of the Grades 3-5 Numeracy Assessment Tool included at the bottom of this post under Assessment.
SUGGESTED YEAR OVERVIEWS
The following are suggested year plans. These year plans take into consideration many aspects of teaching and learning including:
- daily mathematics lesson of about one hour plus other opportunities for mathematics and numeracy experiences throughout the day (such as soft starts, interdisciplinary projects) and connected to other areas of learning
- introducing new and foundational concepts for the grade in the first part of the school year so that there is time to come back to those concepts multiple times throughout the year, considering the importance of spacing in how learning happens
- number sense and computational fluency involve concepts and competencies that are being developed over the entire school year
- within each term or “reporting period” that there is a balance of number-focused content and other areas of math learning so that students are able to show their strengths in mathematics through different concepts
- the curricular competencies are developed over the school year but categories of focus are chosen for instruction, assessment and communicating student learning for each term
- each year plan includes areas of focus for mathematics as well as suggestions for how numeracy can be developed over the school year, with different cross-curricular experiences and numeracy tasks
These year plans are constructed with combined classes in mind with big ideas, concepts and competencies being developed during the same terms across grades in most cases.
Different Lesson Structures and Sample Week Plans
Planning and designing for mathematics teaching and learning involves considering a range of lesson types as well as materials used. Instructional routines such as Number Talks, Splat! or Counting Collections can be taught and then incorporated and extended in plan throughout the school year. More information about instructional routines can be found HERE and HERE.
Most lessons have three parts and you can see this reflected in the example weeks plans included below. The three-part lesson model is based on years of research drawn from the work of Dr. Marian Small and Dr. John van deWalle. In general, the first part of the lesson involves an exploration, instructional routine or task that accesses previous knowledge and language related to the concepts and competencies that are being focused on, the second part investigates the concepts and competencies through tasks and/or problems and the third part focuses on consolidation, sharing and reflection. Sometimes the opening or instructional routine is the first part of a connected lesson but it may also be an additional part. For example, during a unit of study on geometry concept, you may still open your math lesson with a Number Talk as computational fluency is an ongoing focus every week for the whole year. After the Number Talk, you would move into your three-part geometry lesson.
Using a range of lesson types/structures creates varied learning experiences for students. Some different lesson types that you can consider for the teaching and learning of mathematics:
- Problem-based: lesson introduces or reviews key concepts and competencies necessary for students to engage in problem-solving, a problem is investigated and solved and then students share and compare their strategies for solving the problem
- Contextual: a picture book, current event or infographic is used at the beginning of the lesson to contextualize the mathematics to be investigated,
- Math Workshop: after an opening routine or discussion, students choose to practice concepts and competencies through a selected set of tasks, materials or math games that are focused on learning goal/s; the teacher leads small-group instruction during this time
- Math Games: a lesson that focuses on teaching a new math game to the whole class then time to play the game, share and compare strategies and reflect on learning
- Cognitively Guided Instruction (CGI): a lesson that focuses on students solving a contextual problem (number operations) and sharing and recording their thinking with each other; CGI problem types and numberless word problems are examples of this types of lessons
- Materials-based inquiry: a lesson during which students are invited to investigate their own questions about a math concept through different materials and share their connections and findings
In the following sample week plans, you will notice that each week focuses on a key concept throughout a variety of lesson types over the week. A learning goal would be established based on learning standards (content and competencies) and the lessons and tasks for that week would allow for experiences that further develop students’ knowledge and competencies. This learning goal also helps to establish a focus for assessment and goal-setting.
As you can see in the sample week plans, a variety of mathematically structured materials or manipulatives are used, as well as other materials such as land-based found materials or art materials. Suggestions for materials that are available to students in primary, intermediate and secondary classrooms can be found HERE.
As we plan and design for mathematics learning, are planning involves looking at our required learning standards and developing learning goals based on those standards. Those learning goals guide our pedagogical design and are the focus of our assessment. In BC, we are using a four-point proficiency scale. In many cases, it is enough to know whether a student is either proficient or not as this helps to inform our planning for instruction and the supports we create for students. We collect evidence of learning through observations, conversations or interviews, class discussions, and concrete, pictorial or written representations. K-7 Indicators of Proficiency that focus on our BC curricular content learning standards but also incorporate our curricular competencies learning standards in the descriptions of proficiency can be found HERE. These descriptors can be used for communicating students learning as well as self-reflection and goal-setting.
There are foundational number sense concepts and computational fluency questions at each grade level that are developed over the school year. Key assessment questions in these areas can be provided to students once a term to monitor student progress and inform small group instruction. These questions can be found HERE. Note, it is okay to use the same question each term as the focus is on the strategies and application of number concepts which will be developing over the year.
To create a class profile for your class or a more in-depth look at a student’s learning in mathematics and numeracy, our district has developed two assessment tools, with a grade 6&7 assessment tool coming by the end of the 2022-2023 school year.
Many other resources to support mathematics teaching and learning can be found in the pages section of this blog including math games, interdisciplinary projects and numeracy tasks. Richmond teachers can also access many resources through our district portal.
Slides from the August 20 2022 Zoom session:
Link and passcode to Zoom recording:
Please contact me with any questions or suggestions!