# Common Core Math Standards*

A Finch project can meet this standard.

This standard may be difficult to meet with Finch projects.

PE Code Standard Application Related Projects
K.CC.A

Know number names and the count sequence.

Students can count the number of blocks in a program or the number of movements the Finch makes.

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K.CC.B

Count to tell the number of objects.

Students can write a program with a particular number of blocks. For example, they can write a program to make the robot dance using exactly ten blocks. Counting along as the Finch executes each movement in a sequence can also help to reinforce cardinality.

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K.CC.C

Compare numbers.

Students can compare programs to decide which has more blocks.

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K.OA.A

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Students can use the programming blocks as manipulatives to solve simple addition and subtraction problems. For example, the number of movement blocks (arrows), the number of color blocks, and the number of sound blocks will add up to the total number of blocks in the program.

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K.NBT.A

Work with numbers 11-19 to gain foundations for place value.

This standard emphasizes decomposing a number into ten plus some number of ones.

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K.MD.A

Describe and compare measurable attributes.

Students can compare how far the Finch moves for different programs.

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K.MD.B

Classify objects and count the number of objects in each category.

Students can classify the blocks in their program by type and count the number of each. For example, they could distinguish blocks for forward/backward movement from blocks for turning.

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K.G.A

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

This standard focuses on identifying a variety of two- and three-dimensional shapes. Children can draw shapes with the Finch, but Snap! Level 1 can only be used for squares, circles, and rectangles. This may not be sufficient to meet this standard.

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K.G.B

Analyze, compare, create, and compose shapes.

Students can attach a pen to the Finch to draw shapes, as shown in DrawBot. They can compare the shapes created by different programs.

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PE Code Standard Application Related Projects
1.G.A

Reason with shapes and their attributes.

Students can attach a pen to the Finch to draw shapes, as shown in DrawBot. As the Finch turns, it will draw a circle. Challenge students to draw a whole circle, half of a circle, and a quarter of a circle.

DrawBot
1.OA.A

Represent and solve problems involving addition and subtraction.

Students can use the programming blocks as manipulatives to solve simple addition and subtraction problems. For example, students might be challenged to create a program with 20 blocks that contains 12 movement blocks. How many light and sound blocks can they include?

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1.OA.B

Understand and apply properties of operations and the relationship between addition and subtraction.

As noted above, challenges that require students to use specific numbers of blocks will encourage them to add and subtract within 20. This standard will be met as students use different strategies to complete these arithmetic problems.

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1.OA.C

As noted above, challenges that require students to use specific numbers of blocks will encourage them to add and subtract within 20.

Finch Patterns
1.OA.D

Work with addition and subtraction equations.

This standard specifically focuses on understanding the meaning of equations and the equals sign. While similar mathematical expressions can be used in more advanced Finch programming, they are not appropriate for young beginners.

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1.NBT.A

Extend the counting sequence.

Students can count the total number of blocks used by everyone in the class. If they count independently, they can compare their results to reach a consensus.

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1.NBT.B

Understand place value.

In Snap! Level 2, students can measure how far the robot moves at different speeds and compare these values. For example, they can compare the distance moved for three forward blocks at speed 5 and three forward blocks at speed 10.

Measurement Challenge
1.NBT.C

Use place value understanding and properties of operations to add and subtract.

Continuing with the previous example, students can figure out how much farther the robot moved at the higher speed.

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1.MD.A

Measure lengths indirectly and by iterating length units.

Students can measure how far the Finch moves for a forward or backward movement block.

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1.MD.B

Tell and write time.

Create challenges using a large clock face made from posterboard. For example, challenge students to make the robot turn through 40 minutes on the clock.

Finch Tells Time
1.MD.C

Represent and interpret data.

Students can collect a variety of data with the Finch. For example, suppose students write programs to make the Finches dance. As each pair demonstrates their program, students can use tally marks to record which Finches have red beaks, which have blue, and which have green.

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PE Code Standard Application Related Projects
2.OA.A

Represent and solve problems involving addition and subtraction.

In the Measurement Challenge, students can figure out how many blocks are needed to move the robot a particular distance.

Measurement Challenge
2.OA.B

Challenges that require students to use specific numbers of blocks will encourage them to add and subtract within 20. For example, students might be challenged to create a program with 20 blocks that contains 12 movement blocks. How many light and sound blocks can they include?

Finch Patterns
2.OA.C

Work with equal groups of objects to gain foundations for multiplication.

Loops can provide an excellent introduction to this concept.

Repeating Blocks with Finch
2.NBT.A

Understand place value.

In Snap! Level 2, students can measure how far the robot moves at different speeds and compare these values. For example, they can compare the distance moved in millimeters for three forward blocks at speed 5 and three forward blocks at speed 10.

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2.NBT.B

Use place value understanding and properties of operations to add and subtract.

In Through the Maze I, students can measure the length of each section of the maze. They can then add these measurements to calculate how far the robot must move to complete the maze.

Through the Maze I
2.MD.A

Measure and estimate lengths in standards units.

In the Measurement Challenge for Snap! Level 2, students measure how far the robot moves at different speeds.

Measurement Challenge
2.MD.B

Relate addition and subtraction to length.

Continuing with the previous example, students can figure out how much farther the robot moved at the higher speed.

Measurement Challenge
2.MD.C

Work with time and money.

Create challenges using a large clock face made from posterboard. For example, challenge students to make the robot turn through 40 minutes on the clock.

Finch Tells Time
2.MD.D

Represent and interpret data.

For the Measurement Challenge for Snap! Level 2, students can create a bar chart to show how far the robot moves at different speeds.

Measurement Challenge
2.G.A

Reason with shapes and their attributes.

Students can attach a pen to the Finch to draw shapes, as shown in DrawBot. As the Finch turns, it will draw a circle. Challenge students to draw a whole circle, half of a circle, and a quarter of a circle.

DrawBot

PE Code Standard Application Related Projects
3.OA.A

Represent and solve problems involving multiplication and division.

In the Measurement Challenge for Snap! Level 2, students can figure out how many blocks are needed to move the robot a particular distance.

Measurement Challenge
3.OA.B

Understand properties of multiplication and the relationship between multiplication and division.

As noted above, challenges that require students to move a specific distance will encourage them to multiply and divide. This standard will be met as students use different strategies to complete these arithmetic problems.

Measurement Challenge
3.OA.C

Multiply and divide within 100.

As noted above, this standard can be met as students solve real-world problems with the Finch.

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3.OA.D

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Measurement Challenge and Repeating Blocks with Finch require students to use arithmetic to complete Finch challenges.

Measurement Challenge Repeating Blocks with Finch
3.NBT.A

Use place value understanding and properties of operations to perform multi-digit arithmetic.

This standard focuses on achieving fluency with multi-digit addition and subtraction. Finch challenges can require students to use arithmetic to solve real-world problems, but that may not be enough to meet this standard.

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3.NF.A

Develop an understanding of fractions as numbers.

Students can demonstrate their understanding of fractions by programming the Finch to move in a circle divided into equal parts. For instance, the robot could use five equal movements to complete the circle, so that each movement is ⅕ of the circle.

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3.MD.A

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Measurement of volume and mass is not directly related to the Finch. Timing in seconds is important to Finch programming, but this standard focuses on estimation of time in minutes.

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3.MD.B

Represent and interpret data.

For the Measurement Challenge, students can create a bar chart to show how far the robot moves at different speeds.

Measurement Challenge
3.MD.C

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

This standard focuses on calculating area.

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3.MD.D

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Challenge students to move the Finch in a rectangle. They can measure the perimeter of the rectangle and determine how long the robot will need to move to trace out each side.

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3.G.A

Reason with shapes and their attributes.

Use the Finch to partition a circle into parts with equal area. For instance, the robot could use five equal movements to complete the circle, so that each movement is ⅕ of the circle.

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PE Code Standard Application Related Projects
4.OA.A

Use the four operations with whole numbers to solve problems.

A wide variety of Finch projects can require students to solve real-world problems with whole numbers. For example, Play Music with the Finch requires students to use the four operations to scale Finch sensor values to create sounds.

Play Music with the Finch
4.OA.B

Gain familiarity with factors and multiples.

This standard can be incorporated into Remote Control I. For example, if the Finch moves 3 cm forward each time you press the up arrow, can the Finch land on a target 37 cm away?

Remote Control I
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.

Finch Patterns
4.NBT.A

Generalize place value understanding for multi-digit whole numbers.

Understanding and comparing multi-digit whole numbers is essential for any Finch project that uses sensors. The value of the sensor must be compared to a threshold to enable the robot to make a decision.

CricketBot
4.NBT.B

Use place value understanding and properties of operations to perform multi-digit arithmetic.

A wide variety of projects will require students to solve real-world problems using operations with whole numbers. As an example, a student can average low and high sensor readings to find a threshold for the light sensor.

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4.NF.A

Extend understanding of fraction equivalence and ordering.

Students can use the Finch to compare fractions, as shown in Fractions with Finch.

Fractions with Finch
4.NF.B

Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers.

Students can use the Finch to demonstrate how to build a whole circle from unit fractions, as well as how add fractions. Examples are shown in Fractions with Finch.

Fractions with Finch
4.NF.C

Understand decimal notation for fractions, and compare decimal fractions.

The numbers 0-100 are used to control the speed of the wheels 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 full power as a fraction out of 100 or as a decimal. In addition, decimal notation is used for the Finch accelerometers (-1.5g to 1.5g), and the wait time can be expressed as a decimal number of seconds.

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4.MD.A

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

For a project such as Through the Maze I, students can measure the total distance that the Finch must move to make it through the maze. Simple conversions can also be incorporated into a project. 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.

Through the Maze I
4.MD.B

Represent and interpret data.

Students can plot how the distance moved or the angle turned by the Finch changes as the wait time increases.

How Far Will the Finch Turn?
4.MD.C

Geometric measurement: understand concepts of angle and measure angles.

How Far Will the Finch Turn? shows how students can measure the angle turned by the Finch. An understanding of angles is essential for measuring how far the robot turns.

How Far Will the Finch Turn?
4.G.A

Draw and identify lines and angle, and classify shapes by properties of their lines and angles.

As noted above, How Far Will the Finch Turn? shows how students can measure the angle turned by the Finch.

How Far Will the Finch Turn?

PE Code Standard Application Related Projects
5.OA.A

Write and interpret numerical expressions.

Students can write an expression using parentheses and then translate this expression into Scratch or Snap! using math operators. For example, Finch Pong I uses mathematical expressions to make the Finch accelerometer control the movement of a sprite on the computer screen.

Finch Pong
5.OA.B

Analyze patterns and relationships.

Students can program the Finch to increase the brightness of the beak or the pitch of a tone in proportion to the value of a sensor. They can change the constant of proportionality to observe different relationships. One example activity is Play Music with the Finch.

Play Music with the Finch Finch Patterns
5.NBT.A

Understand the place value system.

Understanding and comparing multi-digit whole numbers is essential for any Finch project that uses sensors. The value of the sensor must be compared to a threshold to enable the robot to make a decision.

CricketBot
5.NBT.B

Perform operations with multi-digit whole numbers and with decimals to hundredths.

A wide variety of projects will require students to solve real-world problems using operations with whole numbers. As an example, a student can average several sensor readings to find a threshold for the light sensor.

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5.NF.A

Use equivalent fractions as a strategy to add and subtract fractions.

Students can use the Finch to model this concept, as shown in Fractions with Finch.

Fractions with Finch
5.NF.B

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Students can extend the Fractions with Finch activity to include multiplication and division of fractions. For example, challenge students to make the Finch turn through ¾ of two circles.

Fractions with Finch
5.MD.A

Convert like measurement units within a given measurement system.

Unit conversions can also be incorporated into Finch 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. Alternatively, students can be challenged to measure how far the robot moves in centimeters and convert this measurement to meters.

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5.MD.B

Represent and interpret data.

Students can plot how the distance moved or the angle turned by the Finch changes as the wait time increases.

How Far Will the Finch Turn?
5.MD.C

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

This standard focuses on the measurement of volume. This is not a good fit with the Finch, because the Finch moves in only two dimensions.

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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.

Finch Pong
5.G.B

Classify two-dimensional figures into categories based on their properties.

Students can reinforce their knowledge of different shapes by writing programs to make the Finch draw different shapes.

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PE Code Standard Application Related Projects
6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems.

Ratios can be used to relate values from a Finch sensor to the movement of a sprite on the computer screen.

Finch Pong
6.NS.A

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Students can extend the Fractions with Finch activity to include division of fractions. For example, challenge students to represent ⅓ divided by ¾ with the Finch.

Fractions with Finch
6.NS.B

Compute fluently with multi-digit numbers and find common factors and multiples.

This standard can be incorporated into Remote Control I. For example, suppose one Finch moves 13 cm forward each time you press the up arrow, and another moves 12 cm each time. If they start at the same position, what is the distance to the next position where they both stop?

Remote Control I
6.NS.C

Apply and extend previous understandings of numbers to the system of rational numbers.

The speed of each Finch 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.

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6.EE.A

Apply and extend previous understandings of arithmetic to algebraic expressions.

Students can write an expression using parentheses and then translate this expression into Scratch or Snap! using math operators. For example, Finch Pong I uses mathematical expressions to make the Finch accelerometer control the movement of a sprite on the computer screen.

Finch Pong
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 activity that uses variables; one example is Finch Polygons. In addition, Boolean blocks using the Finch sensors are a good opportunity to talk about substituting values and which values make an expression or inequality true.

Finch Polygons
6.EE.C

Represent and analyze quantitative relationships between dependent and independent variables.

Students can collect data to analyze the relationship between wait time and the angle turned by the Finch, as shown in How Far Will the Finch Turn?. They could also analyze the relationship between wait time and the distance the Finch moves.

How Far Will the Finch Turn?
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 Finch.

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6.SP.A

Develop understanding of statistical variability.

The Finch is an excellent example of the variability inherent to real-world devices. The same commands to the motors may cause a slightly different movement each time. Point out these variations to students and ask them to describe how they affect their projects. Students will also see this variability in How Far Will the Finch Turn?.

How Far Will the Finch Turn?
6.SP.B

Summarize and describe distributions.

Students can quantify the variability associated with the Finch. For example, in How Far Will the Finch Turn?, students can measure how far the robot turns for a given speed and wait time. They can plot multiple measurements and and consider the shape of the distribution.

How Far Will the Finch Turn?

PE Code Standard Application Related Projects
7.RP.A

Analyze proportional relationships and use them to solve real-world and mathematical problems.

The Finch can be used to measure proportional relationships. One example is given in How Far Will the Finch Turn?. Proportions can also be used to relate input from Finch sensors to actions of the motors or changes on the computer screen. Examples are shown in Finch Pong I and Graphing with Finch.

How Far Will the Finch Turn? Finch Pong Graphing with Finch
7.NS.A

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Students can extend the Fractions with Finch activity to include all operations with fractions. For example, challenge students to represent ⅓ divided by ¾ with the Finch.

Fractions with Finch
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 Finch program.

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7.EE.B

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Projects that use variables and math operators will meet this standard. Students can write expressions and equations using variables and then translate them into Scratch or Snap!.

Finch Polygons Finch Spirals
7.G.A

Draw, construct, and describe geometrical figures and describe the relationships between them.

After students draw shapes with the Finch, they can challenge other groups to transform these shapes using translation, dilation, reflection, or rotation (Extension #2 of Drawbot).

DrawBot
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. Students can extend the Finch Spirals activity to compute the circumferences of different circles drawn by the Finch.

Finch Spirals
7.SP.A

Use random sampling to draw inferences about a population.

This standard can be met with projects that use sensors. For instance, in a project using the light sensors, students can take multiple measurements to estimate the amount of ambient light in the classroom.

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7.SP.B

Draw informal comparative inferences about two populations.

This standard can be met with projects that use sensors. For example, to find a threshold for a light sensor, students can take multiple measurements of both the ambient light and a bright light. They can compare these two samples to decide what the threshold should be.

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7.SP.C

Investigate chance processes and develop, use, and evaluate probability models.

Finch activities that use random numbers are a good opportunity to discuss probability. For example, SquirrelBot requires the robot to select one of four different evasive maneuvers.

SquirrelBot

PE Code Standard Application Related Projects
8.NS.A

Know that there are numbers that are not rational, and approximate them by rational numbers.

Irrational numbers cannot be represented in a computer program, because the precision of the computer is limited.

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8.EE.A

Expressions and equations work with radicals and integer exponents.

Exponents can be used to understand how loops work in a program, as shown in Exponents and Loops.

Exponents and Loops
8.EE.B

Understand the connections between proportional relationships, lines, and linear equations.

The Finch can be used to measure proportional relationships. Students can find the relationship between wait time and the angle turned by the Finch, as shown in How Far Will the Finch Turn?. They can also analyze the relationship between wait time and the distance the Finch moves. In addition, proportions can be used to relate input from Finch sensors to actions of the motors or changes on the computer screen. Examples are shown in Finch Pong I and Graphing with Finch.

How Far Will the Finch Turn? Finch Pong Graphing with Finch
8.EE.C

Analyze and solve linear equations and pairs of simultaneous linear equations.

In How Far Will the Finch Turn?, students can calculate the wait time required to produce a particular angle. If students also analyze the relationship between wait time and the distance the Finch moves, then they can calculate the wait time required to move a particular distance.

How Far Will the Finch Turn?
8.F.A

Define, evaluate, and compare functions.

Any Finch 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. Binary with the Finch is an example of a project that can use custom blocks.

Binary with the Finch
8.F.B

Use functions to model relationships between quantities.

Students can measure the relationship between wait time and the angle turned by the Finch. They can use a linear function to model this relationship. An example is shown in How Far Will the Finch Turn?. Linear functions can also be used to relate input from Finch sensors to actions of the motors or changes on the computer screen. Examples are shown in Finch Pong I and Graphing with Finch.

How Far Will the Finch Turn? Finch Pong Graphing with Finch
8.G.A

Understand congruence and similarity using physical models, transparencies, or geometry software.

This standard includes informally understanding that the exterior angles of triangles must add up to 360°. Finch Polygons expands this idea to include the external angles of all polygons. In addition, translation and reflection on the coordinate grid are used to move sprites in Scratch or Snap!, or you can apply these transformations to shapes drawn by the Finch (Extension #2 of Drawbot).

Finch Polygons
8.G.B

Understand and apply the Pythagorean Theorem.

This standard focuses on applying the Pythagorean formula; it cannot be met efficiently with the Finch.

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8.G.C

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

This standard focuses on measuring volume. This is not a good fit with the Finch, which moves in only two dimensions.

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8.SP.A

Investigate patterns of association in bivariate data.

Students can measure the relationship between wait time and the angle turned by the Finch. They can plot the bivariate data and observe the linear relationship. An example is shown in How Far Will the Finch Turn?. Students can also analyze the relationship between wait time and the distance the Finch moves.

How Far Will the Finch Turn?