Grade 3: Lesson Seed 3.OA.8 Using Estimation and Mental Math

Lesson Seed: The lesson seeds have been written particularly for the unit, with specific standards in mind. The suggested activities are not intended to be prescriptive, exhaustive, or sequential; they simply demonstrate how specific content can be used to help students learn the skills described in the standards. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities. These lesson seeds should be adapted to meet the needs of your individual students. Domain: Operations and Algebraic Thinking Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Standard: 3.OA.8 Solve two-step word problems using the four operations. Represent the problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Purpose/Big Idea: Students will use estimation and mental math and to solve a two-step word problem.

Teacher note: You may have to modify your discussion based on how familiar your students are with rounding.

Materials :  Overhead projector or document camera (optional)  Digi-Blocks or base ten blocks  Resource Sheet 7: Fundraising for a Field Trip  Calculators (optional, one per student)  Resource Sheet 2: Directions for Salute (one copy per student)

Activity : Teacher note: Students should use mental math for the warm up problem. You should present problems both vertically and horizontally.

Warm up:  Present a problem on the board, such as: Which answer is closest to the sum of 198 + 74?  Possible choices: o 200 o 300 o 400 o 500  Students should have time to think quietly by themselves in order to determine which answer is correct.

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 Ask the students to share their thoughts and explain why they chose a particular estimate. Ask the students to walk you through their thinking and to share how they solved the problem in their heads.  Ask students to share their reasoning, asking questions such as, “Who can use estimation to explain how they figured this out?” Continue the class discussion so that students understand why 300 is the closest estimate.  Discuss why estimation is an important mathematical skill. Ask students when it would be best to estimate and when it would be best to know an exact number. Discuss when to round up and when to round down.

Activities: NOTE: You can teach this as a whole group lesson or allow students to work at different centers while you teach this to a small group. For a possible center idea, see below.

 Distribute Digi-Blocks or base ten blocks, and Resource Sheet 7: Fundraising for a Field Trip to each student.  Ask the students to put their pens or pencils down and to think about what the problem is asking before beginning. Ask students to use their estimation skills and discuss the problem in groups. Each group should try to determine if the class has raised enough money or not by using mental math. Record students’ estimates on the board.  Facilitate a whole-class discussion or small-group discussion, asking students if the estimates are reasonable. (If students are not using rounding, this would be a good time to discuss rounding as a possible way to find a reasonable solution.)  Allow the students some time to work independently to solve the problem on the Resource Sheet. The students should be encouraged to use any strategy they wish, as long as it is efficient and they can explain their thinking.  You may wish to distribute calculators as your circulate around the room asking questions. The calculators should be used for the purpose of allowing students to check their answers.  Once the students have finished, they should find a partner. The students should discuss whether or not their partners had similar solutions.  For a challenge, students should write the problem as an equation.  Allow time for a few students to share their reasoning with the class or group as you record their thinking on chart paper. (You may prefer to have students share their work using a document camera, if available).  Students should be encouraged to explain why they chose a particular strategy, and why they disagree with another student, if applicable.  Ask questions of the students so that they clarify their thinking. Have someone else in the class explain another student’s strategy and encourage students to apply mathematical relationships.  Ask students how they know their answers are reasonable. Encourage students to discuss whether or not their estimate was close to the actual answer, and to think about strategies that would help them with estimation in the future.  Have a discussion about which strategies students found the most efficient in helping them with estimating and to solve

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problems, and why.

Carefully choosing numbers for the operations can help students focus on developing particular strategies. For example, when working with multiplication, you may prefer to have students work with strategies where they use “friendly” numbers in order to develop strategies that build on using tens. Numbers such as 39 X 3 allow students to think about 40 X 3 and subtract 3 from the product of 120.

Possible Center Activity:  Teach students to play the game Salute to practice math facts. You may use the attached multiplication version (see Resource Sheet 2: Directions for Salute).  Students could record some of their equations in their math journals. The card they choose can be written as the variable, if you have completed the Lesson Plan in this Unit. For example, if they play the multiplication version of the game and their partner shows a three and the solution is 12, the equation would be 3 x C = 12.  You may also modify the game for students who need practice with addition, subtraction, or division facts.  This game can be sent home as homework, as well.

Essential Guiding Questions : These are possible questions to use depending on the discussion. It is not a prescriptive list of questions. The objective is to get students to develop estimation skills and to think about effective problem solving strategies.  Would someone share what they discovered?  How is Sheila’s strategy different from Jose’s? Similar to Jose’s?  Where would you start in solving this problem?  Is this strategy efficient as well as accurate? How do you know?  If this strategy is not efficient to you, what is an efficient method?

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Resource Sheet 7 Fundraising for a Field Trip

Name: ______

A third grade class needs to raise $400 for an upcoming field trip. The class earned $233 dollars at a car wash and $79 collecting can and bottles to recycle. The class also earned $60 at a bake sale. Do they have enough money for the field trip? If not, how much more do they need to raise?

Record your solution using pictures, numbers, and/or words:

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