NUMBERS ABOVE 100

DAY 5

Compact Representations and Exponential Notation

Key Mathematical Ideas

Model numbers greater than 100 using compact representations.
Connect these new figures with exponential notation
Match models with arithmetic descriptions and explain how different representations are equivalent.

This video can be used for the explicit instruction to help you guide children through the tasks.

The key skills and understandings that are highlighted in the video and which you should encourage children to explore as they work with the abacus strings are:

Learning how to model numbers using squares. These models are more compact and can fit on their books.
Learning to describe the square in different ways using the colour-coding system.

Exploration

How can you model the number 235 on the Linear Abacus®? Try using the natural arrangement, then have a go at making a compact model. Describe both models and explain what you notice.

Share their creative thinking on our Mathematics Community Forum

Support

Make a visual reference sheet with children showing the relationship between the expanded and compact models. Have them describe how the model changes and what actions they are using on the abacus string.

Extension

Part 1: Ask children to explain how their linear models, natural models, and compact models are equivalent using arithmetic descriptions to reason.

Part 2: In the compact model, you may have noticed that there are two groups which talk about a group size of ten. If we joined these groups together could you describe what you see in words and with arithmetic descriptions.

Micro Writing Task

Complete day 5 of your journal. For parents and teachers this prompt encourages children to ask questions. As they learn the skill of questioning, they may begin by posing questions:

to find out how to do something
for probing connections- for example why does one thing follow on from another.
to create lines of inquiry
to use as tools of analysis

The latter points, will take time for children to achieve. They need to practice writing and using questions to get to the level where they learn to analyse, direct and clarify their own thinking.