# Common Core Math Standards*

Any Hummingbird project will meet this standard.

A Hummingbird project can be designed to meet this standard by directly demonstrating a concept.

A Hummingbird project can be designed to meet this standard by illustrating a concept.

This standard may be difficult to meet with Hummingbird projects.

#### Grade 4

PE Code | Standard | Application | Related Projects |
---|---|---|---|

4.G.A | Draw and identify lines and angle, and classify shapes by properties of their lines and angles. |
Students can use the servo motor and program the Hummingbird to guide the user through drawing an angle. The program can then identify the angle as acute, right, or obtuse. |
Drawing Angles with the Hummingbird |

4.MD.A | Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. |
Because the Hummingbird will require students to build physical objects, students will naturally measure length, weight, and time in these projects. Simple conversions can also be incorporated into these projects. For example, if the time limit for a program is two minutes, students will have to calculate how many seconds they can use in wait blocks. |
All Projects |

4.MD.B | Represent and interpret data. |
Many projects can include making and interpreting measurements. For example, students can be challenged to build a robot to lift a heavy object as far as possible. Students can measure the distance lifted by various designs and present this data in a graph. |
Lifting a Heavy Load |

4.MD.C | Geometric measurement: understand concepts of angle and measure angles. |
Any Hummingbird project that uses the servo motors will require students to use angles from 0° to 180°. |
All Projects |

4.NBT.A | Generalize place value understanding for multi-digit whole numbers. |
Understanding and comparing multi-digit whole numbers is essential for any Hummingbird project that uses sensors. The value of the sensor must be compared to a threshold to enable the robot to make a decision. |
All Projects |

4.NBT.B | Use place value understanding and properties of operations to perform multi-digit arithmetic. |
A wide variety of Hummingbird projects will require students to solve real-world problems using operations with whole numbers. Example: To find a threshold for the light sensor, a student can average low and high sensor readings. |
All Projects |

4.NF.A | Extend understanding of fraction equivalence and ordering. |
Students can construct a model to illustrate fraction equivalence. |
Illustration of Fraction Equivalence |

4.NF.B | Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers. |
Students can construct a model to demonstrate how to build fractions from unit fractions. |
Illustration of Fraction Equivalence |

4.NF.C | Understand decimal notation for fractions, and compare decimal fractions. |
The numbers 0-100 are used to control the speed of the gear motor and the brightness of the LEDs. These numbers actually represent the percent of full power supplied to the device. Learning more about how these devices are controlled is an opportunity to express the percent of power as a fraction out of 100 or as a decimal. |
All Projects |

4.OA.A | Use the four operations with whole numbers to solve problems. |
A wide variety of Hummingbird projects will require students to solve real-world problems with whole numbers. Example: If the student must move the servo motor from 0° to 180° in 8 steps, he or she must compute the number of degrees for each step and decide what to do with the remainder. This project would use the change blocks seen in the Factor Pairs sketch. |
Factor Pairs |

4.OA.B | Gain familiarity with factors and multiples. |
Students can be challenged to use the change blocks to make the servo motor move in steps from 0° to 60°. How many different step sizes will enable the motor to land directly on 60°? |
Factor Pairs |

4.OA.C | Generate and analyze patterns. |
Any program with a loop creates a pattern! Students can use loops to generate a pattern of lights, sounds, and/or movements. Other students can try to guess the code (the rule) that generates the pattern. |
All Projects |

#### Grade 5

PE Code | Standard | Application | Related Projects |
---|---|---|---|

5.G.A | Graph points on the coordinate plane to solve real-world and mathematical problems. |
Sprites in Scratch or Snap! move on a coordinate plane. Projects that incorporate sprites can be used to meet this standard. For example, students can create a game that uses sensors to control the movement of a sprite. |
Game Controller |

5.G.B | Classify two-dimensional figures into categories based on their properties. |
Students can use the Hummingbird to create a model that illustrates the properties of two-dimensional figures. |
- |

5.MD.A | Convert like measurement units within a given measurement system. |
Because the Hummingbird will require students to build physical objects, students will naturally measure length, weight, and time in these projects. Simple conversions can also be incorporated into these projects. For example, if the time limit for a program is two minutes, students will have to calculate how many seconds they can use in wait blocks. |
All Projects |

5.MD.B | Represent and interpret data. |
Many projects can include making and interpreting measurements. Example: Students can be challenged to lift a heavy object as far as possible. Students can measure the distance lifted by various designs and present this data in a graph. |
Lifting a Heavy Load |

5.MD.C | Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. |
Students can be challenged to use the Hummingbird distance sensor to measure the volume of a box. This project would require Scratch or Snap!. Students can compare the program’s estimate of the volume with measurements made by hand. This will give them an idea of how accurate the distance sensor is. |
- |

5.NBT.A | Understand the place value system. |
Understanding and comparing multi-digit whole numbers is essential for any Hummingbird project that uses sensors. The value of the sensor must be compared to a threshold to enable the robot to make a decision. Students could also use the Hummingbird to create a model that demonstrates their understanding of place value for decimals. |
All Projects |

5.NBT.B | Perform operations with multi-digit whole numbers and with decimals to hundredths. |
A wide variety of Hummingbird projects will require students to solve real-world problems using operations with whole numbers. Example: If the user wants the robot to stop at seven positions between 0° and 120°, he or she must calculate the required angles, which will include rounding decimal numbers. |
All Projects |

5.NF.A | Use equivalent fractions as a strategy to add and subtract fractions. |
Students can construct a model to demonstrate this concept. |
- |

5.NF.B | Apply and extend previous understandings of multiplication and division to multiply and divide fractions. |
Students can be given small challenges, such as moving ⅚ of the way to 180°. These mini-challenges could be embedded in a larger project or used as practice while students are learning to program the Hummingbird. |
- |

5.OA.A | Write and interpret numerical expressions. |
Projects that use math operators in Scratch or Snap! will meet this standard. Students can write an expression using parentheses and then translate this expression into Scratch or Snap!. For example, the Game Controller sketch uses mathematical expression to make the Hummingbird sensors control the movement of a sprite on the computer screen. |
Game Controller |

5.OA.B | Analyze patterns and relationships. |
Students can program the Hummingbird to increase the brightness of an LED in proportion to the value of a sensor. In Scratch and Snap!, they can change the constant of proportionality to observe different relationships and even graph this relationship. This is demonstrated in the Sprite Sizer example. |
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#### Grade 6

PE Code | Standard | Application | Related Projects |
---|---|---|---|

6.EE.A | Apply and extend previous understandings of arithmetic to algebraic expressions. |
Projects that use variables in Scratch or Snap! will meet this standard. Students can write an expression using variables and then translate this expression into Scratch or Snap!. For example, the Game Controller sketch uses mathematical expressions to make the Hummingbird sensors control the movement of a sprite on the computer screen. |
Game Controller |

6.EE.B | Reason about and solve one-variable equations and inequalities. |
This standard includes understanding variables and recognizing when an equation or inequality is true or false. This standard can be met with any Scratch of Snap! project that uses variables. In addition, Boolean blocks using the Hummingbird sensors are a good opportunity to talk about substituting values and which values make an expression or inequality true. |
- |

6.EE.C | Represent and analyze quantitative relationships between dependent and independent variables. |
Students can collect data to analyze how the voltage to the gear motor affects the number of rotations per minute. |
Measuring Motor Speed |

6.G.A | Solve real-world and mathematical problems involving area, surface area, and volume. |
This standard focuses on estimating volume and area by decomposing a complex shape into simple component shapes. This is not a good fit with the Hummingbird hardware. |
- |

6.NS.A | Apply and extend previous understandings of multiplication and division to divide fractions by fractions. |
Students can be given small challenges involving fractions. For example, if you move through half of the range of the servo motor in 5 steps, what is the size of each step? These mini-challenges can be embedded in a larger project or used as practice while students are learning to program the Hummingbird. |
- |

6.NS.B | Compute fluently with multi-digit numbers and find common factors and multiples. |
Students can write a program that finds the least common multiple of two small numbers. The Hummingbird sensors can be used to select the two numbers. |
Least Common Multiples Amusement Park Physics |

6.NS.C | Apply and extend previous understandings of numbers to the system of rational numbers. |
The speed of the gear motor is controlled by an integer between -100 and 100. The sign of the number (positive or negative) controls the direction of rotation. This is a nice application of a number line with positive and negative numbers. |
All Projects |

6.RP.A | Understand ratio concepts and use ratio reasoning to solve problems. |
Ratios can be used to relate values from a Hummingbird sensor to the movement of a sprite on the computer screen. |
Game Controller |

6.SP.A | Develop understanding of statistical variability. |
The Hummingbird is an excellent example of the variability inherent to real-world devices. For example, the value of the distance sensor may change slightly even when an object is stationary. The same commands to the servo motor may cause a slightly different movement each time. Point out these variations to students and ask them to describe how they affect their projects. |
All Projects |

6.SP.B | Summarize and describe distributions. |
Students can quantify the variability associated with the Hummingbird. For example, students can use the distance sensor to measure the distance to a stationary object. They can plot multiple measurements and and consider the shape of the distribution. This demonstration will work best when the object is 50-100 cm from the sensor. |
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#### Grade 7

PE Code | Standard | Application | Related Projects |
---|---|---|---|

7.EE.A | Use properties of operations to generate equivalent expressions. |
This standard focuses on writing expressions in different forms. This is more appropriate for paper and pencil practice, though it is possible that students will need to rewrite an expression to use it in a Hummingbird program. |
- |

7.EE.B | Solve real-life and mathematical problems using numerical and algebraic expression and equations. |
Projects that use variables and math operators in Scratch or Snap! will meet this standard. Students can write expressions and equations using variables and then translate them into Scratch or Snap!. For example, the Game Controller sketch uses mathematical expressions to make the Hummingbird sensors control the movement of a sprite on the computer screen. |
Game Controller Amusement Park Physics |

7.G.A | Draw, construct, and describe geometrical figures and describe the relationships between them. |
Students can meet this standard by making a scale drawing of their robot before they begin to build. This will also encourage students to think through their ideas before they begin construction. |
- |

7.G.B | Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. |
This standard includes computing the circumference of the circle. The Creating Waves with a Gear Motor sketch shows how rotation can be converted to linear motion. In this example, the crankshaft is the radius of the circle. The circumference of this circle determines how far the piston will move. |
Creating Waves with a Gear Motor |

7.NS.A | Apply and extend previous understandings of operations with fractions to add, subtract, multiple, and divide rational numbers. |
Students can be given small challenges involving fractions. For example, if you move through ⅜ of the range of the servo motor in 3 steps, what is the size of each step? These mini-challenges can be embedded in a larger project or used as practice while students are learning to program the Hummingbird. |
- |

7.RP.A | Analyze proportional relationships and use them to solve real-world and mathematical problems. |
The Hummingbird can be used to measure proportional relationships. For example, students can find the linear constant of proportionality that relates the voltage to the speed of the motor. Proportions can also be used to relate input from Hummingbird sensors to actions of the motors or changes on the computer screen. An example is shown in the Sprite Sizer project. |
Measuring Motor Speed |

7.SP.A | Use random sampling to draw inferences about a population. |
This standard can be met with any project that uses a sensor. For instance, in a project using the sound sensor, students can take multiple measurements to estimate the amount of background noise in the classroom. |
- |

7.SP.B | Draw informal comparative inferences about two populations. |
This standard can be met with any project that uses a sensor. For example, to find a threshold for the sound sensor, students can take multiple measurements of both the background noise and a loud sound. They can compare these two sample to decide what the threshold should be. |
- |

7.SP.C | Investigate chance processes and develop, use, and evaluate probability models. |
The Hummingbird kit can be used to create a simple probability model. One example is shown in the Genetics Simulation sketch. |
Genetics Simulation |

#### Grade 8

PE Code | Standard | Application | Related Projects |
---|---|---|---|

8.EE.A | Expressions and equations work with radicals and integer exponents. |
Students can create a game about the rules for exponents. |
Exponent Game |

8.EE.B | Understand the connections between proportional relationships, lines, and linear equations. |
Students can measure the relationship between voltage and motor speed. They can observe that the relationship is linear and use software to see the linear equation. An example is shown in the Measuring Motor Speed sketch. This sketch can be used to address a number of the Grade 8 standards that focus on bivariate data and linear relationships. Proportions can also be used to relate input from Hummingbird sensors to actions of the motors or changes on the computer screen. Examples include the Sprite Sizer project and the Game Controller sketch. |
Game Controller Measuring Motor Speed |

8.EE.C | Analyze and solve linear equations and pairs of simultaneous linear equations. |
Students can extend the Measuring Motor Speed sketch to calculate the motor power or voltage required to produce a particular motor speed. |
Measuring Motor Speed |

8.F.A | Define, evaluate, and compare functions. |
Any Hummingbird project that uses custom blocks in Scratch or Snap! can be used to meet this standard. Custom blocks are analogous to functions in text-based programming languages. Like mathematical functions, they can take an input (parameter) and produce an output (either a number or an action). The comparison between functions in programming and functions in math can help students to understand both of these concepts better. The Factor Pairs sketch is an example of a project with custom blocks. |
Factor Pairs |

8.F.B | Use functions to model relationships between quantities. |
Students can measure the relationship between voltage and motor speed. They can use a linear function to model this relationship. An example is shown in the Measuring Motor Speed sketch. Linear functions can also be used to relate input from Hummingbird sensors to actions of the motors or changes on the computer screen. Examples include the Sprite Sizer project and the Game Controller sketch. |
Game Controller Measuring Motor Speed |

8.G.A | Understand congruence and similarity using physical models, transparencies, or geometry software. |
Students can be challenged to use a linkage to move a small object. This project will require them to think about similar and congruent figures. |
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8.G.B | Understand and apply the Pythagorean Theorem. |
Students can be challenged to use the Hummingbird to design a system that indirectly measures the shortest distance between two points. |
Measuring the Hypotenuse |

8.G.C | Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. |
Students could expand the Measuring the Hypotenuse sketch to design a system to measure the volume of one of these shapes. |
Measuring the Hypotenuse |

8.NS.A | Know that there are numbers that are not rational, and approximate them by rational numbers. |
The Hummingbird cannot represent irrational numbers, because its precision is limited. |
- |

8.SP.A | Investigate patterns of association in bivariate data. |
Students can measure the relationship between voltage and motor speed. They can plot the bivariate data and observe the linear relationship. |
Measuring Motor Speed |