Synopsis

In this lesson, students will learn how to multiply multi-digit numbers by building multiplication structures in Minecraft using partial products. Students should have had practice adding and subtracting multi-digit numbers.
15 x 16 structure - 14.png
Although we ran this lesson with a 5th grade class and had numbers up to the thousands, the problems can easily be adjusted to have students multiply and solve for two- and three-digit numbers.

By creating these multiplication structures, students are able to see the answer first and then understand the process of how to get at it through partial products and knowledge of base ten. While building these structures in the game may take more time in the game than on paper, there is real educational value in students creating their own times table and figuring out how the sums of the part equal the whole.

Learning Objectives

Students will…

Calculate the product of a multi-digit multiplication problem by building out one number horizontally and the other number vertically, and then creating a square structure.
Construct a multiplication structure that clearly shows partial products.
Prove, through articulation and showing of work, how partial products is a process of solving multi-digit multiplication problems.

Standards

Partial Product 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
Operations & Algebraic Thinking	4.OA.A.1 4.OA.C.5
*Numbers & Operations – Base Ten*	4.NBT.A.1 4.NBT.B.5	5.NBT.A.1 5.NBT.B.5

Facilitation Guide

Part 1: Modeling in Minecraft

Setting Up the Problem with Place Values

Note: If students are not familiar with place value and you want to go straight into multiplication, you can skip this section and have students just write down the problem on a sign.

Open up Minecraft in a creative superflat world and project it on the screen for all students to see.
- Note: Change settings to peaceful.
Review place values in Minecraft with students. Please refer to the section “Part 1: Place Value System.”
Once students are able to read and interpret values by place structure, write down multi-digit multiplication problems on the board (e.g. 16 x 15).
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, 16 x 15. 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.

Solving For the Problem

Go through the first problem together with students. We’ll use the problem ’16 x 15′ as an example.
Note: Choose blocks that can be easily counted when they are stacked on top or next to each other. In this lesson, we chose:

Yellow Stained Glass
Light Blue Stained Glass
Magenta Stained Glass
Lime Stained Glass

Length and Height

First, write down ’16 x 15′ on the board.
Now put down 16 blocks horizontally in Minecraft. Then, place 15 blocks vertically, creating an L-shape structure (image below). Note that you’ll only have to place 14 blocks vertically to make 15.

Note that we use yellow stained glass blocks for the first ten blocks of the width and height and different-colored blocks after that. This allows students to easily visualize the numbers.

Now fill in the rectangle with glass blocks –. Your structure should now look something like this:

Explain to students that this is actually the answer to the multiplication problem! By counting the number of blocks, they’ll get the answer.
- However, let them know there is an easier and faster way to calculate the answer rather than counting. This process is called ‘partial products.’
- Ask students if they know what a ‘product’ is. They should eventually say, “An answer to a multiplication problem.”
  - Explain that using partial products will get us to the answer of the multiplication problem.

Partial Product

Have a student volunteer get up on the board with a marker, ready to write down the partial products.
- Note: With partial products, we’ll be asking students to multiply from the tens place first instead of the ones place. This aligns well with the Common Core Standards of focusing on operations in base ten.
Now use these five steps to get them to find the answer. Ask them to:
- STEP 1: Multiply the tens place value of the bottom number with the tens place value of the top number. Ask them what that equals.
  - Now count 10 blocks horizontally and 10 blocks vertically on the bottom left and destroy the area of that length and height. Ask students how many blocks you’ve destroyed (image below). They should say, “100.

Fill it in with the yellow stained glass blocks and use a sign to show work. This is the first partial product.

STEP 2: Multiply the tens place value of the bottom number with the ones place value of the top number. Ask them what that equals.

Ask students, “What is 10 x 5?”

Now count 10 blocks horizontally and five blocks vertically on the top left and destroy the area of that length and height. Ask students how many blocks you’ve destroyed (image below). They should say, “50.”

Fill it in with the light blue stained glass blocks and use a sign to show work. This is the second partial product

STEP 3: Multiply the ones place value of the bottom number with the tens place value of the top number. Ask them what that equals.

Ask students, “What is 6 x 10?”
- Now count six blocks horizontally and ten blocks vertically on the bottom right and destroy the area of that length and height. Ask students how many blocks you’ve destroyed (image below). They should say, “60.”

Now fill it in with magenta stained glass blocks and use a sign to show work. This is the third partial product.

STEP 4: Multiply 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 6 x 5?”
- Now count six blocks horizontally and five blocks vertically on the top right and destroy the area of that length and height. Ask students how many blocks you’ve destroyed (image below). They should say, “30.”

Fill it with lime stained glass blocks and use a sign to show work. This is the fourth and final partial product.

STEP 5: Inform students that the sum of the partial products is the answer to the multiplication problem! Have a student add the partial products on the board, and create a sign to show work.

16 x 15 Partial Product - Step 5.png 15 x 16 structure - 13.1.png

Take a step back to show the set up of the problem and the final partial product structure (image below).

Keeping the partial product structure directly behind the set up of the problem allows for students to show their work and the facilitator to easily check for understanding.

If necessary, go through more examples with students until they become familiar with the method of multiplying multi-digit numbers with partial products and creating the structures.

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.