is the focus of one of the Reasoning and Analyzing curricular competencies from grades K-9. For K-5 the focus is on developing mental math strategies as a means to developing fluent and flexible thinking with numbers. In grades 6-9 the focus is on demonstrating and applying these whole number strategies to new number contexts.
As is the case with all the mathematics curricular competencies, the learning standard is the same for K-5 and then continues for grades 6-9. Grades K-5 focus on the development of mental math strategies while grades 6-9 focus on the application of mental math strategies. The grade level-ness is enacted when the curricular content and curricular competency are connected.
So for example, in grades 6-9, the competency using mental math strategies with whole numbers is applied to decimals in grade 6, integers in grade 7, fractions in grade 8 and rational numbers in grade 9 and it is this intersection of curricular content and competency that is assessed.
The suggested mental math strategies are listed in the elaborations for the curricular content for each grade. Elaborations are suggestions and support for instructional decision-making and are not meant to be used as a requirement or an assessment checklist. Mental math strategies are strategies that are intended for students to be able to do mentally. Computational fluency involves flexible strategy use – both mentally and recorded with paper/pencil, whiteboards, etc. The strategies are transferable to working with larger numbers or to different types of numbers such as fractions and integers. Students may be introduced to the strategies by their peers during a number talk or during an instructional task. When strategies are introduced, specific mathematical language and visual scaffolds such as ten frames or number lines are often used. Some strategies may need to be practiced in different ways before students are able to use them mentally in flexible ways, and choose strategies that make sense for the numbers they are working with. As an example, the following are the computational strategies suggested in the content elaborations for grade 2:
In our 2007 curriculum (WNCP) there was a clear definition of what Mental Math is (in the 2007 iteration of our curriculum, it was named as a mathematical process). “Mental mathematics is a combination of cognitive strategies that enhance flexible thinking and number sense. Mental mathematics enables students to determine answers without paper and pencil. It improves computational fluency by developing efficiency, accuracy, and flexibility.”
Goals of developing fluency with mental mathematics include:
- developing confidence in doing mathematics
- being liberated from calculator dependence
- becoming more flexible thinkers
- be more able to use multiple approaches when problem solving
Strategies develop over time and complement each other. Examples of mental math strategies drawn from the elaborations in our BC curriculum framework include:
- counting on
- making ten
- decomposing (to make tens/hundreds, by place value)
- double and related doubles (doubles plus one, etc)
- bridging over tens (transferable to hundreds, thousands etc)
- adding to find the difference
- commutative, associative and distributive principles
- annexing zeroes
- halving and doubling
Different visual tools can be used to support students’ development of mental math strategies such as ten frames, hundred grids (numbered and blank) and open number lines.
Teachers in Richmond have been developing their own understanding of mental math strategies through Number Talks over the last several years and I believe it is the most used instructional routine in our K-7 classrooms.
The following is a record of some of the number talk experience in Richmond classrooms.
Carrie Bourne and I have started creating a math video series for Richmond educators that our available on our district portal. The series is called Doing the Math Together and the videos are intended support teachers with their understanding of mental math strategies and how they might record students’ strategies during number talks. For example, there are videos in both English and French on the importance of the “making ten” strategy.
They are located in the district portal on the Mathematics page, under the blue tile titled Doing the Math Together Video Series.
Professional resources to support the development of mental math strategies through the development of number talks include:
So what does it mean to be proficient with mental mathematics?
As we begin to work with the new proficiency scale across BC, we need to consider what it means to be proficient with developing, demonstrating or applying mental mathematics in relation to the grade level curricular content. As more teachers across the provinces the the scale, we will have examples of student proficiency that demonstrates initial, partial, complete and sophisticated understanding of the concepts and competencies involved. For example, a grade 2 student at the end of the year would be considered proficient in adding two-digit numbers mentally if they were able to be efficient, accurate and flexible when using two or more different mental math strategies such as decomposing or compensating.
Some questions to consider as you plan for learning opportunities to develop the competency of using mental math strategies:
What strategies or knowledge do students already have about mental mathematics? What opportunities do students have to show and share what they know?
How can we encourage students to be metacognitive when using mental mathematics rather than just applying procedures? How can we develop the concept of efficiency and support students in choosing strategies that are a good fit for the numbers provided?
How can we help students understand the purpose and usefulness of developing mental math strategies?
What opportunities are we creating for students to use mental mathematics across other disciplines such as science or ADST?