Decimals 3E
Overview
In this Phlow, learners explore how multiplying by powers of 10 changes a decimal’s value. Starting with examples such as 506.7 × 10, students decide whether the decimal point moves left or right. Visual arrows and animations demonstrate that multiplying shifts the decimal one place to the right, increasing the number’s size by a factor of ten.
The sequence reinforces understanding through simple, repeatable steps:
- Recognising the correct direction of movement — right for multiplication.
- Crossing out a zero on the 10 to show the one-place shift.
- Understanding that the remaining operation “× 1” leaves the number unchanged.
Through this step-by-step visualisation, learners see that 506.7 × 10 = 5067. The animated transition between numbers helps them connect decimal movement directly to place value principles, building both conceptual understanding and procedural fluency in base-10 operations.
Prerequisite Knowledge Required
- Decimals 3C – Dividing by 10.
- Place Value 2B – Tens, Units and Tenths.
- Understanding that multiplication increases a number’s size.
- Knowing basic multiplication facts for 10 (e.g., 6 × 10 = 60).
- Recognising that the decimal point separates whole numbers and fractional parts.
Main Category
Number & Place Value
Estimated Completion Time
Approx. 8–12 seconds per question (30 questions total). Total Time: 4–6 minutes.
Cognitive Load / Step Size
Low to Moderate — each idea (movement direction, crossing out zeros, interpreting result) is introduced separately. The visual animations anchor understanding in movement and scale, reducing abstraction and strengthening recall.
Language & Literacy Demand
Low — consistent and repetitive phrasing (“move the decimal point,” “multiply by 10,” “to the right”) supported by clear visuals. Symbolic representations replace text-heavy explanations, making the process intuitive and accessible.
Clarity & Design
- Purple arrows highlight the movement of the decimal point.
- Animations show the cause-and-effect of multiplication by 10.
- Handwriting motion visually reinforces the calculation and placement steps.
- Clean, uncluttered screens maintain attention on place value transformation.
Curriculum Alignment
Irish Junior Cycle Mathematics:
- Strand 1 – Number
- Learning Outcomes:
- Multiply decimal numbers by powers of 10.
- Understand and explain how the decimal point moves according to place value.
- Apply multiplication by 10 to scale numbers proportionally.
Engagement & Motivation
The animated “movement” of the decimal makes this Phlow visually engaging and memorable. Each interaction reinforces both understanding and confidence as learners see abstract place value rules come to life in a tangible, predictable pattern.
Error Opportunities & Misconceptions
- Moving the decimal point the wrong direction (left instead of right).
- Adding an extra zero instead of moving the decimal.
- Forgetting that multiplying by 10 increases the number’s size.
- Treating the decimal point as fixed rather than movable based on place value.
Visual comparison between “before” and “after” reinforces the correct pattern and corrects directional confusion.
Transferability / Real-World Anchoring
High — multiplying by 10 supports unit conversions (cm → mm), money calculations, and measurement scaling in science and engineering. It lays essential groundwork for multiplying by 100 and 1000 in later Phlows.
Conceptual vs Procedural Balance
Balanced — students develop procedural fluency (moving the decimal) alongside conceptual insight (each shift equals a tenfold increase). This reinforces their understanding of the base-10 structure of our number system.
Learning Objectives Addressed
- Multiply decimal numbers by 10 accurately.
- Explain how and why the decimal point moves to the right.
- Connect multiplication by 10 to place value changes.
- Recognise how multiplication scales numbers proportionally.
What Your Score Says About You
- Less than 5: You may be unsure about the direction — review how multiplying increases a number’s size.
- 6–7: You’re recognising the rule — practise visualising the decimal shift as scaling up.
- 8–9: Strong understanding — you can apply decimal movement fluently and confidently.
- 10 / 10: Excellent! You can multiply decimals by 10 effortlessly and explain the reasoning — ready for ×100 and ×1000 next.