Tape Diagrams and Equations: IM 6.6.1
[url=https://im.kendallhunt.com/MS/teachers/1/6/1/preparation.html]“Tape Diagrams and Equations”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.6.1
- IM 6.6.1 Lesson: Tape Diagrams and Equations
- Practice 6.6.1
- IM 6.6.1 Practice: Tape Diagrams and Equations
IM 6.6.1 Lesson: Tape Diagrams and Equations
Label the length of the diagram.
Which equation is represented by the diagram above?
Label the length of the diagram.
Which equation is represented by the diagram above?
Draw a diagram to represent the equation 4 + 3 = 7.
Draw a diagram that represents the equation 4 ∙ 3 = 12.
Here is a tape diagram. Which equations match this diagram?[br][br][img]data:image/png;base64,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[/img]
Here is a tape diagram. Which equations match this diagram?[br][br][img]data:image/png;base64,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[/img]
Draw a diagram that represents the equation 18 = 3 + x.
Find the value of the unknown that makes the equation [math]18=3+x[/math] true.
Draw a diagram that represents the equation 18 = 3 ∙ y.
Find the value of the unknown that makes the equation [math]18=3\cdot y[/math] true.
You are walking down a road, seeking treasure. The road branches off into three paths. A guard stands in each path. You know that only one of the guards is telling the truth, and the other two are lying. Here is what they say:[br][br][list][*]Guard 1: The treasure lies down this path.[/*][*]Guard 2: No treasure lies down this path; seek elsewhere.[/*][*]Guard 3: The first guard is lying.[/*][/list][br]Which path leads to the treasure?
IM 6.6.1 Practice: Tape Diagrams and Equations
Here is an equation: x + 4 = 17. Draw a tape diagram to represent the equation.
Which part of the diagram shows the quantity [math]x[/math]? What about 4? What about 17?
How does the diagram show that [math]x+4[/math] has the same value as 17?
Diego is trying to find the value of x in 5 ∙ x = 35. He draws this diagram but is not certain how to proceed. Complete the tape diagram so it represents the equation 5 ∙ x = 35.
Diego is trying to find the value of x in [math]5\cdot x=35[/math]. Find the value of [math]x[/math].
Which equations match to the following tape diagram?[br][img]data:image/png;base64,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[/img]
Which equations match to the following tape diagram?[br][img]data:image/png;base64,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[/img]
Here is an equation: x + 9 = 16. Draw a tape diagram to represent the equation.
Find the unknown value of [math]x+9=16[/math].
Here is an equation: 4 ∙ x = 28. Draw a tape diagram to represent the equation.
Find the unknown value of [math]4\cdot x=28[/math].
A shopper paid $2.52 for 4.5 pounds of potatoes, $7.75 for 2.5 pounds of broccoli, and $2.45 for 2.5 pounds of pears.
What is the unit price of potatoes? Show your reasoning.
What is the unit price of broccoli? Show your reasoning.
What is the unit price of pears? Show your reasoning.
A sports drink bottle contains 16.9 fluid ounces. Andre drank 80% of the bottle. How many fluid ounces did Andre drink? Show your reasoning.
The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of milk has 25% of the recommended daily allowance of calcium. How many milligrams of calcium are in a cup of milk? If you get stuck, consider using the double number line.