Lesson Plan - Multiplying Tenths PDF

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Summary

DGM2 TASK 2: LESSON PLANNING This is the lesson plan for task 2....

Description

Direct Instruction Lesson Plan

General Information Lesson Title: Multiply Tenths by Tenths Subject(s): Math Grade/Level/Setting: 5th grade Prerequisite Skills/Prior Knowledge: It is assumed in this lesson that students understand from fourth grade that “half” means 0.5. Students are taught in fourth grade that the multiplication sign can represent “groups of,” “jumps of,” “rows of,” etc., and can be shortened to “of.”

Standards and Objectives State/National Academic Standard(s): Standard 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor. Learning Objective(s): Given a problem and a 10×10 graph, the student will be able to multiply tenths by tenths using concrete and pictorial representations with 80% accuracy.

Materials

Technology

Hundredths grids, colored pencils, assessment

Learn Zillion video: Multiply a tenth by a tenth

Language Demands Specific ways that academic language (vocabulary, functions, discourse, syntax) is used by students to participate in learning tasks through reading, writing, listening, and/or speaking to demonstrate their understanding.

Language Function(s):

Students will create and analyze models of tenths-by-tenths multiplication. They will explain why

multiplying tenths by tenths equals hundredths.

Vocabulary: Tenths – each of ten equal parts into which something is divided. The place to the right of the ones place in the base-ten system. Hundredths – one of 100 equal parts of a whole. The place directly to the right of the tenths place in the decimal system. Expression – a math sentence with a minimum of two numbers and one math operation

Discourse and/or Syntax: Students will create hundredths grids that represent tenths-times-tenths multiplication problems.

Planned Language Supports:

It is assumed in this lesson that students understand from fourth grade that “half” means 0.5. Students are taught in fourth grade that the multiplication sign can represent “groups of”, “jumps of”, “rows of”, etc., and can be shortened to “of”.

Common Misconception – Students learn that a tenth times tenth is a hundredth; however, students may place the decimal point incorrectly for examples that end with 0. For example, 0.4 x 0.5 is 20 hundredths, but it is also 2 tenths. Students may represent 20 hundredths as 0.020 instead of 0.20

Instructional Strategies and Learning Tasks

Anticipatory Set: Activity Description/Teacher 1. Distribute the hundredths grids and colored pencils to the students. Present the following problem:

Diego’s mother made four pans of brownies

Student Actions 1. Students will reason through the answers using any strategy. a. Many students will verbalize that half of four is two. b. Again, students will say that half of two is one.

and sent half of them to school for Diego’s birthday. How many brownies did Diego take to school?

a. What equation could be written for this situation? Since “half” is “0.5” in decimal notation and “of” means multiply, write 0.5 × 4 = 2 b. Now change the problem so that Diego’s mom made two pans of brownies. How many brownies did Diego take to school? Write 0.5 × 2 = 1 on the board under the first equation. c. Now change the problem so that Diego’s mom made one pan of brownies. How many brownies did Diego take to school? Write 0.5 × 1 = 0.5 on the board under the second equation. What do students notice happens to the product as the total (whole) gets smaller? d. Now change the problem so that Diego’s mom only made half of a pan of brownies. Ask students what expression could represent the situation and write it on the board. The first factor represents the part Diego is taking to school. The second factor represents the half of a pan of brownies that his mom made.

c. Students will say that half of one is a half. They notice the product gets smaller. d. 0.5 × 0.5. Read the expression together as a class “half of half” or “five tenths of five tenths”

Presentation Procedures for New Information and/or Modeling: Activity Description/Teacher 2. Have students locate the first hundredths grid on their papers and explain that one square represents a pan of brownies. a. Write 0.5 to the left of the square. This amount represents the part Diego took to school. b. Write 0.5 on the top of the square. This amount represents the half of a

Student Actions a. Write 0.5 to the left of the square. This amount represents the part Diego took to school. b. Write 0.5 on the top of the square. This amount represents the half of a pan of brownies that his mom made. c. With one color (red), shade five tenths columns (the amount Diego’s mom made).

pan of brownies that his mom made. c. With one color (red), shade five tenths columns (the amount Diego’s mom made).

d. With a different color (blue), shade five tenths rows (the amount Diego took to school). d. With a different color (blue), shade five tenths rows (the amount Diego took to school).

e. Where the two colors overlap (purple); 0.25, 25 hundredths, or some students may say 1/4. e. Where is the product represented?

3. Student responses may vary.

3. Write the answer 0.25 next to the expression on the board and ask students what they observe about the product when multiplying a number less than a whole by another number less than a whole. Guided Practice: Activity Description/Teacher 4. Present the following problem. Ask students what expression best represents the situation and write it on the board. Mrs. Miller, an interior designer, is making a throw pillow for a customer. She has a piece of fabric that is 0.4 yards. She uses 0.2 of the 0.4 yards. How much fabric (in yards) is she using?

Student Actions 4. Write 0.2 × 0.4 or 2/10 × 4/10 5a. Write 0.2 to the left of the hundredths grid and 0.4 on top of the hundredths grid. b. Shade in four tenths with one color (four columns). It represents the original piece of fabric. c. Use a different color and shade the two tenths (two rows). It represents the piece Mrs. Miller

cut off for the pillow. 5. Have students follow the same steps as in the previous example.

d. Where the two colors overlap is eight hundredths.

b. What does this represent?

e. Students are taught in fourth grade that the multiplication sign can represent “groups of”, “jumps of”, “rows of”, etc. and can be shortened to “of”. This is one reason it is suggested that students shade the vertical column first so they can say, “I need two tenths of the four tenths that I already have.”

c. What does this represent? d. Where is the product represented? e. Why? Recall the way the expression was read: “two tenths of four tenths.”

6. Present the following problem and repeat the steps above to evaluate: Lucas and Eva are walking to school. Their school is 0.8 miles from their house. So far, they have walked half of the way (0.5) to school. How far have they walked?

a. Ask students what expression best represents this situation and write it on the board. b. Write 0.5 to left of the hundredths grid and 0.8 on top of the hundredths grid. c. Shade in eight tenths with one color (eight columns). What does this represent? d. Use a different color and shade the five tenths (five rows). What does this represent? e. Where is the product represented? f. How else can 40 hundredths be written or read? g. The expression is read as “five tenths of eight tenths” but can also be read “half of eight tenths.” Therefore, it makes sense that the answer is four tenths.

6a. 0.5 × 0.8 or 5/10 of the 8/10 b. Write 0.5 to left of the hundredths grid and 0.8 on top of the hundredths grid. c. Shade in eight tenths with one color (eight columns). It represents the total miles from home to school. d. Use a different color and shade the five tenths (five rows). It represents the distance the children have walked so far. e. Where the two colors overlap is 40 hundredths f. 0.4 or 4 tenths

Independent Student Practice: Activity Description/Teacher Give the students the “Multiplying Tenths”

Student Actions Students will complete the “Multiplying Tenths”

worksheet.

worksheet.

Culminating or Closing Procedure/Activity: Activity Description/Teacher

Student Actions

Show the Learn Zillion video “Multiply a tenth by a tenth”.

Differentiated Instruction Consider how to accommodate for the needs of each type of student. Be sure that you provide content specific accommodations that help to meet a variety of learning needs.

Gifted and Talented: For students who need a challenge, have them use the commutative property and shade two hundredths grids – one for each factor pair. Another suggestion is to have students explore how to represent the examples in the lesson using base-ten blocks.

EL: For students who need help understanding what tenths and hundredths mean, use a dollar to represent a whole, dimes as tenths, and pennies as hundredths.

Students with Other Special Needs: For students who are struggling at present with the problem 0.4 × 0.3, have students use a flat base-ten block to represent the hundredths grid. Use two index cards. Place one index card on top of the flat to show three tenths vertically (the card should cover seven tenths). Place the second card on top of the flat to show four tenths horizontally (the card should cover six tenths). The two cards together form and “L” shape to expose the array and product of 12 hundredths.

For students who need additional instruction to understand that 0.5 is a half, write 0.5 as a fraction (5/10). Draw a square, partition it into 10 pieces, and shade 5 of the pieces. Show how this is equivalent to 1/2.

Assessment Formative

Students will show that they understand multiplying tenths by tenths equals hundredths by completing a worksheet where they will use a hundredths grid to complete tenths-times-tenths problems. They will analyze a model to identify the expression represented within the model and explain why multiplying tenths by tenths equals hundredths.

Summative (Quizzes, Tests, products)...