Working With Advanced Fractions
Advanced fraction work on task cards, for the point where fractions stop being pieces of a circle and start being numbers that can be added, compared and turned into each other. That transition is where most children lose fractions, because the material that made them obvious is put away just as the arithmetic gets hard. Task cards keep the work going without an adult supplying every problem. Durable plastic with rounded corners. In English.
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Working With Advanced Fractions introduces mathematical relationships through color-graduated blue sectors that children physically arrange and compare.
- Recognizes fraction relationships through color-coded blue sectors
- Combines and compares different fraction pieces to form wholes
- Discovers equivalent fractions through hands-on manipulation
- Develops fraction vocabulary through concrete experiences
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Each fraction circle divides into precise segments, enabling hands-on exploration of parts and wholes before symbolic representation. The blue gradations create visual harmony while distinguishing each fraction family - halves appear in one shade, thirds in another, allowing immediate recognition of equivalent relationships. Young mathematicians manipulate these paper sectors to discover that two halves equal one whole, three thirds complete a circle, revealing fraction concepts through direct sensorial experience. The fan arrangement of segments invites systematic exploration, as children naturally progress from matching identical pieces to combining different fractions. This tactile approach to fractions honors the child's need to touch and move objects while building mathematical understanding, establishing concrete experiences that later transform into abstract fraction work with symbols and operations.
How to present it
Follow the Montessori method of presentation for optimal child development.
Arrange the fraction circles on a mat with sectors organized by denomination. Place whole circles on the left, followed by halves, thirds, quarters, progressing to smaller divisions. Ensure each blue gradation group stays together.
- 1
Introduce the whole circle first, tracing its complete edge with your finger
Use slow, deliberate movements to emphasize the concept of 'one whole' - 2
Present halves by placing two semi-circles together to recreate the whole
Let the child feel the straight edge where pieces meet - 3
Explore thirds by counting aloud as you place each sector: 'one third, two thirds, three thirds make one whole'
Point to each piece as you count to reinforce one-to-one correspondence - 4
Invite the child to match sectors by their blue shades, creating complete circles
Start with larger fractions (halves, thirds) before introducing smaller divisions - 5
Compare different fractions by overlaying sectors: 'Which is larger, one half or one third?'
Let the child discover relationships through direct comparison rather than explanation
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