# 6th Grade Task: Gears

6th Grade Task: Gears

### Standards & Objectives

Academic standards
CCSS.Math.Content.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same...
CCSS.Math.Content.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to...
CCSS.Math.Content.6.NS.C.7
Understand ordering and absolute value of rational numbers.
CCSS.Math.Content.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and...
CCSS.Math.Content.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings...
CCSS.Math.Content.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0, and use rate language in the context of a ratio relationship....
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,...
GLE 0606.2.3
Understand and use ratios, rates and percents.
GLE 0606.3.6
Understand and use the Cartesian coordinate system.
SPI 0606.2.6
Solve problems involving ratios, rates and percents.
SPI 0606.2.7
Locate positive rational numbers on the number line.
SPI 0606.2.8
Locate integers on the number line.
SPI 0606.3.9
Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
TSS.Math.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or...
TSS.Math.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent...
TSS.Math.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value...
TSS.Math.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, the ratio of wings to beaks...
TSS.Math.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0. Use rate language in the context of a ratio relationship.
TSS.Math.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems.

Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.

Essential and guiding questions:

Whole Group Questions:

PART A:

• Who can explain how you know that gear B will turn fewer times than gear A? Does it matter how many times gear A turns – will gear B always turn fewer times? Why?

PART B:

• Many of you created a table to record the turn values. Why was this an effective way to keep track of the turns?
• What are some of the patterns that you noticed?
• How did this table help you establish a relationship between the number of turns?
• What is the relationship between gear turns?
• Did anyone find another way to keep track of the gear turns?
• Was it more useful than a table?

PART C:

• Who can explain how you determined the number of times gear A would turn if gear B turned once? Who used the table? How did that help?
• Who set up an equation? How did you determine what equation to use? Who used a ratio and scaled through division or multiplication? How are these methods related to each other?

PART D:

• Who initially thought you would add 4 teeth to both gears? Why?
• What made you change your mind? If 4 teeth are added to gear A and 6 teeth are added to gear B, how does that connect to the relationship you saw in part B?

### Activity/Task Variations

Blooms taxonomy level:
Understanding
Differentiation suggestions:

Entry/Extensions:

Assessing and Advancing Questions

If students can’t get started….

Assessing Questions

• Let’s look the gears. As gear A turns, tell me what will happen to gear B. Why?

Advancing Questions

• If gear A turns all the way around, will gear B also turn all the way around? Why or why not?

If students finish early….

Assessing Questions

• Show me how you determined your answer to part D.

Advancing Questions

• If gear B turns 117 times, how many times will gear 1 turn? How do you know?
• If a third gear C was added and connected to gear B with 15 teeth and gear A turned 5 times, how many times would gear C turn?