Grade 7 · Combine rational changes · 357 of 750
Combine rational changes · practice 38
Start at 8 and apply a signed change of 6.5. Where do you finish? Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Start at 8 and apply a signed change of 6.5. Where do you finish?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
A positive change moves right; a negative change moves left.
Work through the reasoning
Step 1
Translate the givens
The initial position is 8; the signed displacement is 6.5, so write 8 + (6.5).
Step 2
Calculate with the model
Starting at 8, move 6.5 units right. The endpoint is 14.5.
Step 3
Check and interpret
Undo the displacement: 14.5 − (6.5) = 8. This recovers the starting position.
The answer
8 + (6.5) = 14.5.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
The mathematical idea
A signed change has both size and direction. Start at the original value and move right for a positive change or left for a negative one. The endpoint is a sum, while the distance traveled is the absolute value of the change. Starting quantities: Starting value = 8; Signed change = 6.5.
final = start + signed change
03 · Reflect and transfer
Explain what changes and why.
Why is the sign of a change different from the sign of the starting position?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.