Synopsis

This lesson plan should be facilitated after students are familiar with place value, and have had practice adding and subtracting multi-digit numbers. We also recommend that students are familiar with partial products and how place values are represented in Minecraft.
Mathcraft Place Values.png
Although we ran this lesson with a 5th grade class and had numbers up to the thousands place, the problems can easily be adjusted to have students multiply and solve for two- and three-digit numbers.

In this lesson, students are challenged to multiply multi-digit numbers by building them in Minecraft. Using their knowledge of place value (ones, tens, hundreds, and thousands), they must create the problem in the game and solve for them.

While creating these multiplication structures in the game may take more time than on paper, it provides students with a visual representation and tactile experience as they are digitally building the answers. Through guided facilitation and constant practice, students will come to a better understanding about how the ones, tens, hundreds, and thousands place values are related to one another.

Learning Objectives

Students will…

Read and interpret the place value number system. This is accomplished by:
1. Understanding how to say the number through place value. For example, they can see three blocks in the “hundreds” place, two blocks in the “tens” place, one block in the “ones” place, and be able to say, “That’s 321.”
2. Recognizing that one block in the “tens” place equals to ten blocks in the “ones” place and is one-tenth of a block in the “hundreds” place.
Construct multiplication problems with multi-digit numbers and their answers by going through multiple calculation steps and articulating their response.

Standards

Place Value Multiplication Structures Standards Alignment
Click on the link above to view our explanations of how this lesson plan is aligned to Common Core Math Standards.

Grade Level	4th Grade	5th Grade
Domain
*Numbers & Operations – Base Ten*	4.NBT.A.1	5.NBT.A.1 5.NBT.B.5

Facilitation Guide

Part 1: Place Value System

Open up Minecraft in a creative superflat world and project it on the screen for all students to see.
- Note: Change settings to peaceful.
Set up a value in the game for the thousands place, hundreds place, tens place, and ones place.
- Note: Choose blocks that can easily be counted when they are stacked on top of each other. For example, we chose:
  - Ones place: Pumpkin
  - Tens place: Polished Andesite
  - Hundreds place: Lapis Lazuli
  - Thousands place: Polished Granite
- Ask students if they know what value is being represented (example below).

In this example, the place values go from (left to right) thousands, hundreds, tens, and ones. Notice how individual blocks are easy to count when stacked on top of each other.

When one student gets it right, ask them how they know. For the example above, they should say something along the lines of:
- “There’s two blocks in the thousands place so that’s 2000.”
- “Four blocks in the hundreds place so that’s 400.”
- “Eight blocks in the tens place so that’s 80.”
- “Five blocks in the ones place so that’s 5.”
- “Add them together and it’s 2,485.”
If necessary, set up additional values until students are able to explain their answers.

Now set up a value in the game where there’s more 10 or more blocks one of the place values. For example, you can place 14 blocks in the tens place value (image below).

Have students count how many blocks are in the tens place value and ask them what number that equals to.

Ask students what that value is. They should say, “14 tens or 140.”
Show them how to carry. If there’s 10 or more blocks in one place value, that equals one block in the place value to the left. Destroy those ten blocks, replace them with glass blocks, and put one block on the place value to the left (image below).

The glass blocks represent the values we “carried” over to the place value to the left . Showing the work this way provides students with a visual understanding of the place value number system.

Part 2: Modeling in Minecraft

Setting Up the Problem

Once students are able to read and interpret values by place structure, write down multi-digit multiplication problems on the board (e.g. 26 x 21).
Ask them how they would set up the problem in Minecraft. At this point, you can do the first example with the class. After that, have them set up the rest of the problems and walk around to check if they’re doing it correctly.

This is the set up for the multiplication problem, 26 x 21. Note how the places values for the number are lined up. The granite blocks are used as a multiplication and equal sign, and are placed on the right side.

We’ve provided some sample problems along with images of what the setup looks like and the answers. The sample problems can be accessed here:
Mathcraft-PLC ™ – Multi-digit Multiplication Structures_Place Values.pdf
- Download
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.

Solving For the Problem

Go through the first problem together with students. We’ll use the problem ‘26 x 21′ as an example. As students suggest answers, build it in Minecraft while having a student volunteer write the equation and show the steps on the board. We’ve provided the steps and images of what it looks like in Minecraft below. Note: Place the blocks behind the set up of the problem in their correct place value.
- First, ask them where the ones place is and the tens place is.
- Now use these five steps to get them to find the answer. Ask them to multiply:
  - STEP 1: The ones place value of the bottom number with the ones place value of the top number. Ask them what that equals.
    
    Ask students, “What is 1 x 6?”
  - STEP 2: The ones place value of the bottom number with the tens place value of the top number. Ask them what that equals.
    
    Ask them what they are multiplying. A common answer (and a misconception) may be, “1 times 2.” Make sure that students understand the 2 is in the tens place so it’s, “1 times 20.”
  - STEP 3: The tens place value of the bottom number with the ones place value of the top number. Ask them what that equals.
    
    Students should be able to say, “This is 20 times 6.”
  - STEP 4: The tens place value of the bottom number with the tens place value of the top number. Ask them what that equals.
    
    Students should be able to say, “This is 20 times 20.”
    - Note: As students go through each step, build that value in Minecraft so they can see what it looks like. Don’t worry about “carrying” just yet. Just keep placing the blocks down in the correct place value even if the total number of blocks exceeds 10.
  - Now ask students if there’s anything they need to “carry.” In this example, there shouldn’t be. Ask them what the value is (546).
  - If necessary, go through more examples with students until they become familiar with the method of multiplying multi-digit numbers.

The final equation should look similar to this image.

Note: In our class, a student said he knew of the Lattice Method, which is a different way of multiplying. I asked him to show the class how it worked, and although not all students understood the Lattice Method, I felt it was an important learning opportunity for the student to share his knowledge, and for the class to know there are multiple ways to solve for a problem.

Part 3: Students Building in Minecraft

Write down different multi-digit multiplication problems for the students.
Get all students in Minecraft (individually if possible) and tell them:
- Set up these problems in the game.
- Solve for them and build the answer directly behind the problem.
- Put up a sign that shows the work (alternately, students can show their work on paper)
Feel free to assign problem sets to specific students or student groups, since they’ll all be building in the same world.
As students are building, walk around the classroom to see if students are understanding how to solve the problems and that they are on-task.