Estimate Products

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Objective

SWBAT use estimation and multiplication to check reasonableness of answers and solve real world problems.

Big Idea

Students use estimation to check answers as well as explore estimation in real world contexts.

Warm Up

5 minutes

Students will start today's lesson with a fluency assessment.  This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.

This is an assessment I have my students do each week and then graph their results.  It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions.  (It also happens to be the quietest time in my math classroom all week!!) 

This is what my classroom looks like as students work on this assessment.

 

 I do not start my students with the fourth grade skills. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards.  By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics.  I want to make clear that this assessment ONLY measures basic math computation.  It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year.  Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.

 Please check out the resources to hear my thoughts about students fluency progress: progress monitoring graph.

 Note:  Students will begin the fourth grade set next week.

Concept development

40 minutes

The Common Core Standards include estimation skills for every grade level.  We’re interested in using language with children that includes such words and phrases as about, close, just about, a little more (or less) than, and between.  From a 10,000 foot view, we want our students to be able to do the following mathematically:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

In real life, estimation is part of our everyday experience.  When you’re shopping in the grocery store and trying to stay with in a budget, for example, you estimate the cost of the items you put in your cart to keep a running total in your head.  When you’re purchasing tickets for a group of people or splitting the cost of dinner between 8 friends, we estimate for ease.  Contractors or consultants often work in a world of estimates.  Rarely do we know all the facts up front and there could be many variables at play.  Therefore, a ballpark number is perfectly sufficient.

- See more at: http://mylearningspringboard.com/why-teaching-both-estimation-and-accuracy-is-important-in-math-instruction/#sthash.P2AcD4S2.dpuf

The Common Core Standards include estimation skills for every grade level.  We’re interested in using language with children that includes such words and phrases as about, close, just about, a little more (or less) than, and between.  From a 10,000 foot view, we want our students to be able to do the following mathematically:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

In real life, estimation is part of our everyday experience.  When you’re shopping in the grocery store and trying to stay with in a budget, for example, you estimate the cost of the items you put in your cart to keep a running total in your head.  When you’re purchasing tickets for a group of people or splitting the cost of dinner between 8 friends, we estimate for ease.  Contractors or consultants often work in a world of estimates.  Rarely do we know all the facts up front and there could be many variables at play.  Therefore, a ballpark number is perfectly sufficient.

- See more at: http://mylearningspringboard.com/why-teaching-both-estimation-and-accuracy-is-important-in-math-instruction/#sthash.P2AcD4S2.dpuf

The CCSS include estimation skills for every grade level.  Using language with students that include such words and phrases as about, close, just about, a little more, a little less, and between are important in order for students to gain an understanding about using estimation.   

In every day life, or the real world as I sometimes say, estimation is part of our everyday experience.  When you’re shopping in the grocery store and trying to stay with in a budget, you estimate the cost of items you put in your cart to keep a running total in your head.  When you’re purchasing tickets for a group of people or splitting the cost of dinner between 8 friends, we estimate for ease. 

Estimation is a very important skill for students to be proficient in. I want my students to be able to determine the reasonableness of their answer.  Without estimation skills, students are not able to determine if their answer is within a reasonable range.  This inability to reason causes them to make computational errors without them having any idea they've made an error.   If a student is asked to multiply 22 x 34 and they arrive at a product of 86, I want students to independently recognize that 86 could not  possibly be a reasonable answer.  If they use the estimation of 20 x 30 to arrive at 600, they quickly realize that they've made a mistake.

I begin this lesson by telling students that estimation is used  all the time and for different purposes. I remind students that they rounded when adding and subtracting in our last unit; it was one strategy to help check the answer. I tell students that they can also use rounding in multiplication to estimate products. Together, we practice checking double digit by double digit multiplication by estimating first to note a reasonable answer for the actual product.   

I then remind students that in every day life, estimation is great for giving educated guesses about possible amounts. You might see a pile of boxes and estimate that there are about 2,500 toys. It's okay if the actual number is 2,479. You were close enough for a quick idea. 

For the remainder of the lesson, students work with their learning partner to solve the four problems on the multiplication estimation page in the resource section.  Then, partners share their thinking and work with the document camera.  I lead a class discussion centered around each problem and ask questions like:

What would be the result if you estimated to the lower ten?  Why could that be problematic?

In question 3, does this estimate follow the rounding "rules" you've learned in the past? (1,2,3 or 4 round down, 5,6,7,8 or 9 round up)  

 I lead the class to a conclusion that estimation is determined by the situation.  This is an important shift for some students who have memorized the above rounding rule with little contextual understanding. 

The Common Core Standards include estimation skills for every grade level.  We’re interested in using language with children that includes such words and phrases as about, close, just about, a little more (or less) than, and between.  From a 10,000 foot view, we want our students to be able to do the following mathematically:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

In real life, estimation is part of our everyday experience.  When you’re shopping in the grocery store and trying to stay with in a budget, for example, you estimate the cost of the items you put in your cart to keep a running total in your head.  When you’re purchasing tickets for a group of people or splitting the cost of dinner between 8 friends, we estimate for ease.  Contractors or consultants often work in a world of estimates.  Rarely do we know all the facts up front and there could be many variables at play.  Therefore, a ballpark number is perfectly sufficient.

- See more at: http://mylearningspringboard.com/why-teaching-both-estimation-and-accuracy-is-important-in-math-instruction/#sthash.P2AcD4S2.dpuf

 

In the following video, you can hear a students thinking about problem 2 on the worksheet.  This student is struggling with the concept of estimation to make "friendly" or "easier" numbers. 

 

 In this video, you can observe a students thinking about problem number one.  

 

 

Student debrief - Wrap up

7 minutes

As a wrap up, students write for 3 minutes in their math journals and brainstorm as many ways as they can, when a person might use estimation. I start them off by telling them this morning I got up at about 5:00 am.  I emphasize the word about noting that this is an estimate.  After the three minutes, students share their lists with their learning partner.