## Using estimation in multiplying two-digit numbers

**Standards **

CCSS.MATH.CONTENT.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operation … Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

## Time

This lesson takes 40 minutes to an hour, depending on how long you allot your students to complete each of the 4 problem sets and whether you have students play the game.

## Technology Required

Computer with a projector, Smartboard or other device for your class to watch videos or videos can be shared in Google meet or other application for remote learning. Spirit Lake: The Game can be downloaded and played on Windows or Mac computers. An iPad version will be available by Fall 2021. Schools that are part of the Growing Math project or who have a 7 Generation Games site license will have access to all of these games for students to use at home or school.

## Optional Recommended Resource

Use resources like the Helping Math Multiplication Worksheet Generator to make your own worksheet. Their worksheets look very much like this one on multiplication of two-digit numbers with Easter egg examples, except with many more activities in each worksheet. Note that the link will require you to register for a free download. Registration takes about 1 minute. You’ll then receive a link to download over 100 free worksheets on math topics from addition to rational numbers. Another resource we like is the Lizard Point math worksheet generator. Both will print the worksheets as well as the answer key. Note that sites using PRINT TO Google Drive may have that feature disabled after December, 2020. However, you can still from the PRINT menu select SAVE AS PDF, download a file as PDF and then upload it to your Google Drive. The Growing Math project has no affiliation with Helping Math or Lizard Point.

## Summary

You’ll need 20 math problems multiplying two-digit numbers. You can use math problems you already have or use one of the online worksheet generators. Based on research showing the effectiveness of distributed practice – that is, practicing a skill for more, shorter periods rather than one long session – we have students solve a few problems at a time, with videos in between. The lesson begins with a brief explanation of multiplying two digit numbers, followed by students solving 3-5 problems multiplying two-digit numbers. Students then watch a 3-minute video that works an example of multiplying a three-digit number by a two-digit number. They then solve 3-5 more problems, followed by another video, then more problems. We recommend giving a time frame – say, 7-10 minutes – to solve the problems rather than set number of problems because this allows you to begin and end each section of the lesson with all of the students at once.

## Lesson Plan

### 1. Introduction to Multiplying Two-digit Numbers

Begin with an example from Helping with Math, that gives an explanation of multiplication and a variety of types of problems. Then, have the students try to solve 3 to 5 problems. You can use those included in the Google slides linked or create your own.

### 2. Video : Multiplication and Estimation

#### Estimation is one of the most practical math skills!

There are a lot of math concepts that I use regularly when writing software or computing statistics in my day job. The one skill I use all the time is estimation. (I can tell you that the ability to accurately estimate an answer is not universal.)

In the problem in the video above, we start out by multiplying 892 x 11, using the fact that any number multiplied by 10 is just that number with an added zero. To test our answer, we round 892 to 900 and can estimate that our answer should be near to – and less than – 9,900.

Let’s say you type the wrong number in your phone, hitting the 6 instead of the 9, since these two are pretty close and you have big fingers. Now your answer is 7,612. If you have a good grasp of estimation and multiplication, that is clearly wrong. If you’re computing how much money you need to charge a customer based on the 892 hours you expect to work at $11.00 per hour, you have just lost out on over $2,000!

### 3. More multiplication problems

Now that you have had a little practice and a little instruction, students solve another 3-5 problems.

### 4. Video : Multiplication and Estimation

This video works through a problem multiplying a 3 -digit number by a two-digit number . It also gives a strategy for solving difficult problems. That is, break the problem into smaller, easier problems.

Here, because the last digit of one number is 7 and of the other number is 2, you know that 7 x 2 = 14. So, whatever else your answer is, it has to end in a 4.

### 5. Follow up to the video

As a math teacher, I heard approximately 4,897,234 times from students:

WHY do I have to do so many problems of the same type?

– Almost every student I ever taught math

Explain to students that all of those facts learned, like 2 x 7 =1 4 are the basis for the commutative property of multiplication, reducing numbers to lowest terms, or solving equations by multiplying or dividing both sides by a constant, and more. You need a BASE to work from, problems that can be examples.

The fact is that the more experience you have with numbers, the more problems you solve. The more problems solved, the easier it gets.

### 6. Finish off by a few more math problems

Now that you’ve watched another video, it’s time for the last set of math problems.

### 7. Optional – Game Play

Students can Spirit Lake: The Game . Multiplying two- and three-digit numbers comes up in Level 4. We recommend allowing students to play for 15-30 minutes each session. This gives them enough time to get started but not enough time to get bored.

## Assessment

Answers to the 12 -20 math problems completed by the student provide one assessment. A second assessment is in the reports for the Spirit Lake game, which show whether students answered correctly the problems in Level 4, whether they read the hint before answering the problem, and whether they were correct on the first try or had to attempt the problem more than once.

### State Standards

**Minnesota Math Standard 4.1.1.3** – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

**Minnesota Math Standard 5.1.1.4** – Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.