# Introducing our Engage Activities for the IB: Real-world mathematics to foster inquiry and develop problem-solving skills

We believe that the right classroom structures are essential to ensuring that all students have a mathematical voice in the classroom. Our Engage Activities have been specifically designed to do just this, and we are very excited to be able to now add these to our IB textbooks for MYP and DP.

We believe that the right classroom structures are essential to ensuring that all students have a mathematical voice in the classroom. Our Engage Activities have been specifically designed to do just this, and we are very excited to be able to now add these to our IB textbooks for MYP and DP.

First of all, let's take a look at the structure of our Engage Activities:

**Hook**

The Hook opens the learning activity with a predictable structure and familiar context, designed to promote mathematics agency. Routines reduce cognitive load for students and remove barriers to entry.**Launch**

Having sparked interest and curiosity, this section encompasses two slides: the activity introduction slide and the grouping instructional slide.

The activity introduction slide ensures that all students have access to the mathematical content at hand, provides opportunities for the important activity of student questioning and clarification, and, as a result, opportunities for teacher scaffolding. The grouping slide details the routine students will utilize.**Explore**

Students explore the activity and begin independent problem solving. The teacher takes on the powerful role of an observer or facilitator and begins to address misconceptions - making use of the teacher support materials identifying common misconceptions and purposeful questions where appropriate.**Discuss**

The purpose of this stage is to engage students in mathematical discourse, something shown to be beneficial in numerous studies. Students will present their own thinking as well as observe, question, discuss, and learn from the mathematical thinking of their peers.**Reflect**

Students have an opportunity to reflect on their learning after each Engage Activity - an exercise of metacognition, the value of which is again based on a wealth of research. Insights are shared with teachers to inform next steps in instruction.

With the structure as outlined above, and the research justification for that structure, hopefully it is clear that our Engage activities have been carefully designed to support effective teaching and learning of mathematics. What is particularly exciting with the release of these activities to our IB books, is how well this aligns with the philosophy and requirements of the IB syllabus.

All 8 of our IB-aligned books, covering MYP and DP, now contain Engage Activities to give students the opportunity to investigate and explore a variety of mathematical concepts as well as practice for the MYP assessments and the DP internal assessments.

**General alignment MYP:**

Completing the Engage Activities in the MYP books will not only enhance a students’ knowledge and understanding (Criterion A) of the mathematical concept, but they will practice identifying and describing patterns and rules (Criterion B), communicating mathematically with their group and during their presentation (Criterion C) and apply the mathematical concepts to real-life problems (Criterion D).

**Specific examples MYP:**

In the IB MYP 2 textbook, the Building algebraic expressions Engage Activity requires students to build algebraic expressions (Criterion A) for their own game which they must design and describe (Criterion C) and model with an algebraic rule (Criterion B).

In the IB MYP 3 textbook the Applications of Pythagoras' theorem engage activity requires students to apply Pythagoras’ theorem (Criterion A) to solve a real-life problem (Criterion D) and justify their choices in their solution.

In the IB MYP 4 textbook Trigonometric ratios engage activity requires students to apply the trigonometric ratios (Criterion A) to solve a real-life problem (Criterion D).

In the IB MYP 5 textbook and the IB MYP 5 Extended textbook the Line of best fit engage activity requires students to find a line of best fit (Criterion A) for nutritional data to examine and describe (Criterion C) the relationship between calories and macronutrients (Criterion D).

**General alignment DP:**

For the DP courses, the IB Core, Analysis and Approaches, and Applications and Interpretation textbooks contain engage activities to assist students in preparing to lead their own investigation when they complete their internal assessment/exploration.

All engage activities require students to present their work in writing and to the class (Criterion A). These presentations require mathematical communication skills (Criterion B). Students often need to think independently and creatively to come up with their own methods and solutions (Criterion C). Some engage activities require students to reflect on the appropriateness of their solution in the provided context (Criterion D). And of course, all engage activities require a use of the appropriate mathematical concept (Criterion E).

**Specific examples DP:**

In both the IB Analysis and Approaches SL textbook and the IB Applications and Interpretation SL textbook the Applications of quadratics using graphs engage activity requires students to model the path of a basketball with a quadratic (Criterion E) equation and consider what factors determine whether the ball goes through the hoop (Criterion D).

If you don’t already have access to Mathspace, and would like to explore our Engage activities, simply request access here.