#### MathematicalExplorationsFour

MatExFour
Ages 9 to 10

Exploring Geometry & Triangles Tessellating Triangles
Stage: 2
This problem encourages children to use the right vocabulary when talking about shape properties. They will begin to understand that, for a shape to tessellate, the angles where they come together are important. Tiles on a Patio
Stage: 2
Working on this investigation provides many opportunities to speak with youngsters to discover how they are going about generating new ideas. The activity encourages growth in problem solving, spatial awareness and number awareness. Fractional Triangles
Stage: 2
This problem could be used as part of a lesson on finding fractions of various shapes. It should help develop an understanding of the relationship between the part and the whole. It allows children to explore fractions in anon-threatening, open-ended way and yet it does contain some real challenge.

Investigating Fractions and Number

Simplest fractions

This is the first problem in a set of three linked activities. Egyptian Fractions and The Greedy Algorithm follow on.

It's often difficult to find interesting contexts to consolidate addition and subtraction of fractions. This problem offers that, whilst also requiring students to develop and analyse different strategies and explain their findings.

Skills and concepts experienced: Fractions. Algebraic fractions. Visualising. Curious. Generalising. Calculating with fractions. History of number systems. Creating expressions/formulae. Mathematical reasoning & proof.

Egyptian Fractions

Unit fractions are the first fractions children meet, and here we discover some very surprising and interesting characteristics of these familiar numbers. Some of these characteristics were known to the ancient Egyptians whilst other conjectures are yet to be proved.

Whilst meeting both old and new mathematical ideas, students can improve their fluency in addition and subtraction of fractions and be challenged to generalise and explain their findings.

Skills and concepts experienced: Mathematical reasoning & proof. Calculating with fractions. Generalising. Algebraic fractions. Creating expressions/formulae. History of number systems. Interactivities. Visualising. Fractions

The Greedy Algorithm

This problem follows on from Keep It Simple and Egyptian Fractions

These three problems together offer students an opportunity to engage with some mathematical ideas in depth and not just with the rather mechanical process of adding and subtracting fractions.

This problem in particular requires students to compare fractions and may deepen their understanding of their relative sizes.

Skills and concepts experienced: Calculating with fractions. Visualising. Equivalent fractions, decimals and percentages. Fractions. Resourceful. Creating expressions/formulae. History of number systems. Generalising. Curious.

Consecutive negative numbers

This problem could replace a "standard practice exercise" for adding and subtracting negative numbers. It provides opportunities for a lot of calculation, in a context of experimenting, conjecturing, testing conjectures, etc.

Skills and concepts experienced: Addition & subtraction. Creating expressions/formulae. Games. Generalising. Curious. Positive-negative numbers. Visualising. Making and proving conjectures. Working systematically.