Objective:

Students will learn to represent two-digit numbers using place value while applying basic computational thinking through algorithms. They will break down a number into tens and ones, and create step-by-step algorithms to model their thinking.

Materials Needed:

• Tens blocks (e.g., bundles of 10 straws or base-10 blocks)

• Ones blocks (single cubes or counters)

• Algorithm cards (sequence cards with basic commands like "Pick up 1 block," "Group 10 ones into a ten," "Repeat")

• Chart paper for group work

Steps:

• Introduction:

  • Begin by asking students, “How can we break down the number 23 into tens and ones?” 

  • Write a two-digit number on the board and explain that numbers can be broken into parts using simple algorithms, or step-by-step instructions. 

  • Demonstrate with physical manipulatives how to decompose 23 into two groups of ten and three ones.

• Group Activity:

  • In small groups, students will use manipulatives to represent their assigned numbers. 

  • Alongside the hands-on activity, students will write down an algorithm or sequence of steps explaining how they decomposed their number. 

  • For example, if they’re working with the number 45, their steps might include "Pick up four tens blocks," "Pick up five ones blocks," and "Group 10 ones to form a ten."

• Expanding and Practicing:

  • Once students have their numbers represented with blocks, they will swap their algorithms with other groups. 

  • Groups will follow their peers’ algorithms to reconstruct the numbers. 

  • This will help students see how step-by-step thinking leads to correct results.

• Discussion and Reflection:

  • Each group will present their number and algorithm to the class, discussing how following specific steps helped them break down the number accurately.

Equity and Access:

Provide extra visual aids and simplified algorithm steps for students who need more guidance. Encourage peer support for those who may find following or creating algorithms challenging.

Real-World Application:

Connect this lesson to real-world tasks like grouping items in a store or organizing supplies, explaining how systematic steps (algorithms) help us achieve our goals more efficiently.

CS Practice(s):

• Developing and Using Abstractions: Students decompose numbers into tens and ones, creating abstract representations of quantities.

• Recognizing and Defining Computational Problems: Students define a problem (breaking a number down) and use an algorithm to solve it.

• Creating Computational Artifacts: Students create a written algorithm (sequence) to model their thinking and guide peers through a task.

Standard(s):

• CA CCSS Mathematics 1.NBT.B.2

• CA CS K-2.AP.10

Objective:

Students will use Scratch Jr. or another coding platform to program an animation that models the place value of two-digit numbers, demonstrating tens and ones through code. They will use loops and sequences to create a digital representation of place value, learning computational thinking as they design their programs.

Materials Needed:

• Tablets or computers with Scratch Jr. installed

• Digital images of tens and ones blocks

• Pre-made templates for number models

Steps:

• Introduction:

  • Start by reviewing the concept of place value and how two-digit numbers are made up of tens and ones. Introduce Scratch Jr. as a tool for creating digital models of numbers. 

  • Explain that students will be building programs that show how numbers are constructed from tens and ones using simple programming commands.

• Group Activity:

  • In pairs, students will choose a two-digit number. 

  • They will then use Scratch Jr. to create an animation where the computer breaks down their number into tens and ones. 

  • For example, if the number is 32, students will program the animation to show three tens blocks and two ones blocks appearing on the screen.

• Creating and Coding:

  • Guide students through using loops and sequences to automate their animation. 

  • For example, they can use loops to repeat the action of creating a "ten" three times and placing it on the screen. 

  • Students will create sequences that follow a logical order: first the tens, then the ones. 

  • Encourage students to troubleshoot errors as they go by running the program and adjusting their code.

• Testing and Refining:

  • Once students finish their programs, they will test the animation by running it and checking if the sequence of events correctly represents their number. 

  • Students will collaborate in refining the code if needed by debugging issues such as misplaced blocks or incorrect loops.

• Presentation and Discussion:

  • Each pair will present their completed Scratch Jr. animation to the class, explaining the sequence of their program and how it accurately models the tens and ones of their number. 

  • Lead a discussion on how coding helps us represent mathematical concepts visually.

Equity and Access:

Provide pre-made Scratch Jr. templates for students who need extra support in getting started. Pair students with varying levels of programming experience to ensure collaborative learning.

Real-World Application:

Discuss how programming concepts like sequences and loops are used in everyday tasks such as designing computer systems, organizing data, or creating video games, emphasizing that coding helps simplify complex tasks.

CS Practice(s):

• Creating Computational Artifacts: Students use Scratch Jr. to create digital animations representing place value.

• Testing and Refining Computational Artifacts: Students test their programs and refine their code to ensure correct representation of tens and ones.

• Collaborating Around Computing: Students work in pairs to create, test, and improve their programs, learning how to solve problems together.

Standards:

• CA CCSS Mathematics 1.NBT.B.2

• CA CS K-2.AP.10