Our exciting work at HappyNumbers.com doesn’t just happen in front of a computer screen – it takes place in the classroom as well. As we interact with students at all levels, we often find the opportunity to explore non-standard solutions or build mathematical logic. These discoveries have inspired us to develop the Extended Thinking Series, a set of supplemental resources for each topic that will provide a fun challenge for students and push them to use higher-order thinking skills. Enjoy and subscribe to our blog for more Extended Thinking Series ideas!
Our recent post Numeration 1-10: Taking it Further was so well-received by students and teachers that we couldn’t wait to bring you more! These challenging but grade-appropriate tasks are a great way to encourage higher-order thinking while bringing depth and rigor to fundamental math skills. And we’re pleased to announce the release of Plus & Minus to 5: Taking it Further:
This supplemental resource can be used during the topic Plus & Minus to 5 to push high-achieving students or to challenge the entire class!
Although your primary students may be just learning to add and subtract small numbers, they can begin to develop algebraic thinking with this fun exercise. We’ve combined simple, familiar equations with helpful graphics to make algebra accessible to even the youngest mathematicians. By replacing the unknowns with eye-catching bags of candy, an equation like x + x = 4 is more concrete and kid-friendly.
This task takes students beyond the basic knowledge-level skill of addition and requires them to use strategic analysis of the problem. First, students must realize that two identical bags hold the same amount of candy. Then, they may discover that each bag must hold fewer than 4 candies, since the total of both bags is 4. From there, students may try a guess-and-check approach or rely on their growing recollection of equations. The final two problems on Plus & Minus to 5: Taking it Further provide even greater challenge by adding a loose candy to the equation. Now, essentially, students are solving x + x + 1 = 5.
Students who struggle to solve the exercises could be encouraged to draw candies to help find the solution. You may even decide to take the task ‘off paper’ by using manipulatives to help struggling learners. A child-size sock makes a great ‘candy bag’ for counters or cubes.
The new standards have pushed teachers to require students to articulate mathematical thinking, and this advanced exercise provides a perfect opportunity to do so. Students who attempt to explain an incorrect solution are likely to catch their own error. Those who have solved the problems correctly can further their math skills by explaining their process to a peer, a teacher, or the class.
The demand for advanced exercises has shown us that teachers are looking for fun, engaging ways to help students look at math from a different perspective. We hope that this latest offering will meet that need and help your students grow in their understanding of mathematics. Let us know how it goes in your classroom and if you have any creative ideas for using this exercise in different ways.
And check back soon for more Extended thinking exercises!
Happy Numbers Team