Lesson

Objective:

Students will use number cards to physically represent and compare multi-digit numbers. By arranging digits according to their place value and discussing how digits shift when multiplied or divided by ten, students will reinforce their understanding of place value while practicing computational thinking.

Materials Needed:

• Number cards (1–9)

• Place value mats labeled with “ones,” “tens,” “hundreds,” “thousands”

• Math problem cards with multi-digit numbers to compare and arrange

• Whiteboards for students to record comparisons using >, =, or < symbols

Steps:

• Introduction:

  • Start by discussing how each place in a multi-digit number represents ten times the value of the place to its right. 

  • For example, the digit 5 in the hundreds place is ten times what it would represent in the tens place.

  • Introduce the activity where students will physically manipulate number cards to build and compare large numbers based on place value.

• Group Activity:

  • In small groups, students will receive a set of number cards and a place value mat. 

  • They will draw math problem cards with two multi-digit numbers (e.g., 453 and 329). 

  • Students will place the digits on the mat according to their place values, then compare the numbers by discussing how the values of each digit determine which number is larger or smaller. 

  • They will record their comparison using >, =, or < symbols.

• Pattern Recognition:

  • As students work with the number cards, guide them in recognizing patterns in place value. 

  • For example, they might notice that shifting a number by one place (e.g., moving a digit from the tens to the hundreds place) increases its value by ten times. 

  • Encourage students to explain these patterns in their own words, reinforcing both mathematical and computational thinking skills.

• Presentation and Discussion:

  • Groups will present their number comparisons to the class, explaining how the place value of each digit influenced the comparison. 

  • They will also reflect on how the place value patterns helped them make decisions about the numbers.

Equity and Access:

Provide number lines or base-ten block illustrations to support students who need help visualizing place value concepts. Offer differentiated number sets for varying levels of difficulty.

Real-World Application:

Connect place value to real-life contexts, such as understanding large numbers in technology (e.g., how computers store large quantities of data using place value systems like binary).

CS Practice(s):

• Recognizing and Defining Computational Problems: Students break down number comparison tasks into smaller steps by analyzing place value.

• Developing and Using Abstractions: Students abstract the concept of place value using physical number cards.

Standard(s):

• CA CCSS Mathematics 4.NBT.2

• CA CS 3-5.AP.13

Objective:

Students will use a robot, such as Sphero or Bee-Bot, to navigate through a series of challenges that help them recognize how place value works in multi-digit numbers. As students program the robot to move according to the values in each digit, students discuss how each place represents ten times what it represents to its right, reinforcing computational thinking concepts.

Materials Needed:

• Sphero or other robots

• Grid map labeled with place values (ones, tens, hundreds, thousands)

• Math problem cards with multi-digit numbers for students to compare and program robot movements

• Tablets or computers for programming the robots

Steps:

• Introduction:

  • Begin by reviewing the concept of place value, emphasizing how a digit in one place represents ten times what it represents in the place to its right. 

  • For example, discuss how the number 700 is ten times 70. 

  • Then introduce the robot challenge: students will program their robot to travel across a grid, where each space represents a place value (e.g., hundreds, tens, ones).

• Programming the Robot:

  • In pairs, students will be given a multi-digit number (e.g., 753). 

  • They must program the robot to move according to the values of each digit, starting from the hundreds place and moving down to the ones. 

  • For example, the robot might move 7 spaces for the hundreds place, 5 spaces for the tens place, and 3 spaces for the ones place. 

  • They can also program comparisons between numbers by programming the robot to stop at symbols like “>,” “=,” or “<” on the grid.

• Testing and Refining:

  • Once the robot is programmed, students will test it on the grid. 

  • They check if the robot moves according to the correct place value of each digit. 

  • If the robot moves incorrectly, students will debug their code and refine it until the movement matches the number's place value correctly.

• Presentation and Discussion:

  • Each group will present their programmed movements to the class, explaining how the robot’s movements correspond to each place value. 

  • Encourage discussion on why certain movements were necessary and how this relates to understanding large numbers.

Equity and Access:

Provide visual supports like number lines or base-ten block illustrations for students who need extra guidance. Pair students with varying levels of programming experience to ensure collaborative learning.

Real-World Application:

Discuss how place value concepts are essential in computer systems that handle large numbers and data sets. Understanding place value helps in coding and organizing information in digital formats.

CS Practice(s):

• Creating Computational Artifacts: Students create a program that models place value using a robot.

• Testing and Refining Computational Artifacts: Students test and refine their robot’s movement to ensure it accurately represents the place value of numbers.

Standard(s):

• CA CCSS Mathematics 4.NBT.1

• CA CS 3-5.AP.12

• CA CS 3-5.AP.13

• CA CS 3-5.AP.17