How do Gizmos Support the Standards for Mathematical Practice?

The Standards for Mathematical Practice (SMP) rest on important “processes and proficiencies” with longstanding support from leading mathematics education organizations and researchers. Gizmos are ideal for incorporating these standards into the learning experience. With accompanying Lesson Materials providing the guiding questions, students use Gizmos to develop both the knowledge and the general mathematical capabilities that lead to long-term success.

In-Depth Exploration of the Practices: Function Machines Gizmo

Consider the Function Machines Gizmo. In this Gizmo, students are introduced to the concept of functions and function tables, using colorful input-output machines. Students program machines with function rules to create input-output tables. In addition, students have the ability to stack machines, create composite functions, and even program their own machines!

In addition to supporting the Common Core Content Standards 5.OA.3, 8.F.1, F.IF.1, and F.BF.4.a., the Function Machines Gizmo supports almost all of the Standards of Mathematical Practice:

STANDARDS FOR MATHEMATICAL PRACTICE (SMP) & HOW THE FUNCTION MACHINES GIZMO SUPPORTS THE STANDARD

HOW THE FUNCTION MACHINES GIZMO SUPPORTS THE STANDARD

1Make sense of problems and persevere in solving them.

Students are challenged to determine what a machine does, or 'solve' it, based on input-output pairs. Challenging problems can be created by stacking machines.

2Reason abstractly and quantitatively.

Students use abstract reasoning while looking at number patterns on charts and graphs. Students use quantitative reasoning to determine each machine's the specific function rule.

3Construct viable arguments and critique the reasoning of others.

Students discuss methods of solving machines and interpreting input-output data. Students can challenge each other to solve machines they have programmed.

4Model with mathematics.

Many real-world situations can be modeled with the Function Machines Gizmo, such as how revenue and profit depend on sales, or how distance traveled depends on time.

5Use appropriate tools strategically.

Several tools are available to help students solve their function machines. Students can program a machine to see if its output matches a mystery machine. They can also view machine input-output pairs on a table or plotted on a graph.

6Attend to precision.

Students use appropriate terminology of input and output in discussion and reasoning with others.

7Look for and make use of structure.

Patterns of input-output values help students determine how each machine functions.

8Look for and express regularity in repeated reasoning.

Students identify the pattern of the function machines to come up with rules, and develop strategies for solving new machines.

Sample Gizmos and Supported SMP

Every mathematics Gizmo in our library supports teaching the Standards for Mathematical Practice.

Polygon Angle Sum

Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged.

SMP: 1, 2, 3, 7, 8

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.

SMP: 2, 5, 6, 7

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake.

SMP: 1, 2, 3, 4, 5

No Alien Left Behind (Division with Remainders)

The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This is a nice illustration of division with remainders.

SMP: 2, 4, 6, 7, 8

Cannonball Clowns (Number Line Estimation)

Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing your clown-launching skills on a number line, move on to the Big Top, Football Field, School Buses, the Golden Gate Bridge, and more!

SMP: 2, 6

Road Trip (Problem Solving)

Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities.

SMP: 1, 3