https://file.aiquickdraw.com/mathbot/file/1728854149179a73kct3p.jpg

To create more questions similar to the one in the image, I'll use the following format, which focuses on determining the gradient (or slope) of a line based on how many squares it moves up for each square it moves across.

Here are five new questions:

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1. **New Lines to Analyze:** Draw five new lines on a similar grid. Label them F, G, H, I, and J. Then, answer the following questions:

   a) For every 1 square across, line F goes ___ squares up.  
      The gradient of line F is ___.

   b) For every 1 square across, line G goes ___ squares up.  
      The gradient of line G is ___.

   c) For every 1 square across, line H goes ___ squares up.  
      The gradient of line H is ___.

   d) For every 1 square across, line I goes ___ squares up.  
      The gradient of line I is ___.

   e) For every 1 square across, line J goes ___ squares up.  
      The gradient of line J is ___.

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2. **Slope Comparison Questions:** Given lines with the following gradients, rank them from steepest to least steep.

   - Line K with a gradient of 2
   - Line L with a gradient of -1
   - Line M with a gradient of 0.5
   - Line N with a gradient of -2
   - Line O with a gradient of 1

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3. **Negative and Positive Slopes:** 

   a) Draw a line with a positive slope of 3 on a grid.
   b) Draw a line with a negative slope of -2 on a grid.
   c) Identify which of the lines you drew is the steepest, and which one descends the most quickly.
   d) Explain why one line moves up as it goes to the right, while the other moves down.

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4. **Fractional Gradients:** 

   Draw lines on a grid that have the following fractional gradients. For each one, describe the movement across and up:

   - Gradient of 1/2
   - Gradient of -1/3
   - Gradient of 3/4
   - Gradient of -1/4
   - Gradient of 2/3

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5. **Real-World Gradient Application:**

   Imagine a hill represented on a map grid. For every square the hill goes across, it goes 2 squares up.  

   a) What is the gradient of the hill?  
   b) If a different path goes up 1 square for every 3 squares across, is this path steeper or gentler than the first path? Explain.  
   c) Describe another real-world scenario where gradients are used to describe the steepness of a path or slope.

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**Tip:** When calculating gradients, always remember that a positive slope means the line rises as it goes right, while a negative slope means it falls as it goes right.

Explore how to calculate the gradient of lines on a coordinate grid. Learn about positive and negative slopes, fractional gradients, and how steepness changes depending on slope values. This lesson provides new questions with examples suitable for students in Grades 6-8.

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