“Estimate reasonably” is one of the mathematical curricular competencies under Reasoning and Analyzing, the first strand of curricular competencies. The curricular competency of being able to estimate reasonably is a learning standard at every grade level from K-12. Because the curricular competencies in mathematics are not grade specific, they need to be connected to curricular content to be assessed and evaluated at grade level. For example, estimating reasonably:
- at Kindergarten could be estimating within quantities to 10,
- at grade 4 it could be computational estimation when adding and subtracting numbers to 10 000 or estimating the order of fractions along a number line using benchmarks
- at grade 8 it could be estimating answers when calculating with fractions, estimating the surface area and volume of regular solids or estimating best buys when using coupons (financial literacy)
Curricular competencies to connect to many areas of curricular content but not all. When planning mathematical learning experiences, it is important to consider what competencies complement the content. For example, there are connections to estimating working with number concepts such as quantities, fractions and percentages as well as computational estimation, financial literacy and measurement.
Another consideration is that because this curricular competencies is the same essentially from K-12, it can be used as an access point for all students when planning for multi-age or cross-grade classes, developing IEPs and looking at class profiles.
What does it mean to be able to estimate reasonably?
As students begin their development of competency in estimation, they are comparing quantities as being more than or less than a known quantity. This further develops in using a referent for estimating such as if you know a handful of cubes is 10 cubes, you can use this information for estimating the total quantity of cubes in a jar. Likewise, a personal referent of knowing the size of your step that is about one metre long can help you to estimate distances. As students develop a strong sense of number, they are able to estimate within a reasonable range, knowing which numbers are too high and too low. As students become more competent with estimation and knowledgeable about quantity and other math concepts they are able to apply more abstract estimation strategies such as approximation and rounding.
How can we assess a student’s competence in estimating reasonably?
The Lower Mainland Mathematics Contacts network began to develop assessment tools to use with students to assess the curricular competencies. A draft of the estimating tool is here and teachers might find it a helpful starting place in thinking about how estimation develops along a continuum and the types of “I can” statements that can be used with students for self-assessment:
Estimating Ideas – LMMC DRAFT 2016
This assessment tool is still in draft form as we put this project on hold while the Ministry was developing a classroom assessment framework. General information about the classroom assessment framework, developed in collaboration with teachers, can be found HERE and the information specific to mathematics can be found HERE. The mathematics classroom assessment framework includes criteria categories and descriptors as well as examples from across grade levels. The Ministry is now using a four-point proficiency scale to provide descriptive feedback to where students are in their development.
Some resources to support competency development in estimation:
Andrew Stadel curates a website called Estimation 180 that is full of estimation tasks with a photograph as a starting point. Students are asked to consider what number would be too low and then which would be too high to develop their reasoning around what a reasonable range would be.
Many “three-act tasks” involve an element of element. Both Graham Fletcher and Dan Meyer have archived videos and examples of three-act tasks.
Steve Wyborney has developed a series of estimation tasks using photographs called Estimation Clipboard. You can download the slides and find more information about this instructional routine HERE.
For our BCAMT Reggio-Inspired Mathematics project, we have create a pedagogical content knowledge four-pager about estimating. You can download it here:
Two favourite picture books that focus on estimation, with a focus on using visual referents are Great Estimations and Greater Estimations by Bruce Goldstone.
Other picture books to connect to estimation:
How Many Seeds in a Pumpkin? by Margaret McNamara
Counting on Frank by Rod Clement
Betcha! by Stuart J. Murphy
Some questions to consider as you plan for learning opportunities to develop the competency of estimating reasonably:
Do students understand what it means to estimate, that there is reasoning involved?
How can we connect the curricular competencies of estimating and visualizing? Are students scanning quantities and using visual referents? How can we encourage students to explain their strategies and make what they are doing in their mind visible?
What opportunities can we create for students to make adjustments to their original estimates based on new information? Are they making meaning of the situation?
What opportunities are we creating for students to think about estimation across math content areas – number, quantity, measurement, financial literacy and other areas in context?