Lesson Plan 

Name: Candace Willis Date: November 29, 2004  Age/Grade Level: 2nd Grade

 Subject: Mathematics  # of Students: 25  # of IEP Students: 4

 Major content: Algebraic Ideas  Unit Title: Block Pounds

 

ACTIONS

 Goals and Objectives-

Students will explore the use of variables as unknowns as they solve for the weights of objects using information presented in pictures. They will model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

 Connections-

Students will:

  • solve problems involving variables as unknowns;
  • replace variables with numbers to solve problems;
  • recognize pictorial and equation representations of the same relationship;
  • write addition equations for relationships presented in pictures

This lesson covers the following Algebra Standard Expectations:

  • Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
  • Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
  • Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

 

Based on the Kentucky Mathematics Standard (MA-E-4.3.1) of how patterns (e.g., numbers pictures, and words) are alike and different.

           

Context-

Block Pounds introduces students to the use of variables in the equations and to ways to solve equations by applying the techniques of replacement, addition, and subtraction, all of which are central to algebraic thinking. Representing pictures by using sets of addition equations sets the stage for the translation of words into symbols, an important skill in solving algebraic problems presented in stories. Finally, when students describe and record their solution steps, they are learning to document and reflect on their reasoning, a skill central to all learning.

 

 Resources-

Materials needed:

  • A pan balance,
  • Small wooden cubes,
  • A "Block Pounds" activity sheet for each student, and
  • A chalkboard or other classroom board or poster board

 Procedures-

Draw the picture of the two weight scales in figure 2.2 on the board. Label the scales A and B, as shown. Tell the students that these are scales and that they show the weights of the blocks that have been placed on them. Ask the following questions:

  • (Point to scale B.) What is on scale B? (a sphere) How much does it weigh? (six pounds)
  • (Point to scale A.) What is on scale A? (a cube and a sphere) How much do the objects weigh all together? (nine pounds)
  • Figure out the weight of the cube. How did you do it? (The sphere is 6 pounds, so the cube weighs 9 - 6, or three, pounds.)

Draw the two scales for weight problem 2 (fig. 2.3) on the board or on poster board. As in problem 1, the weight of one block is given in this problem. But unlike in problem 1, to find the weight of a cube, two operations must be performed. First the total weight of the cubes must be determined. Then the weight of each cube must be found. Ask the following questions:

  • What block is on scale A? (a sphere)
  • How much does the sphere weigh? (four pounds) How do you know? (The scale shows four pounds.)
  • (Point to scale B.) What is on scale B? (one sphere and two cubes)
  • How much do the blocks weigh all together? (fourteen pounds)
  • (Point to the sphere on scale B.) How much does this sphere weigh? (four pounds)
  • How can you figure out how much each cube weighs? (The sphere is four pounds. So the two cubes are 14 - 4, or ten, pounds. So each cube weighs five pounds.)

Point out to the students that the blocks of the same shape have the same weight. So since the sphere on scale A weighs four pounds, the sphere on scale B must also weigh four pounds. In like manner, the cubes weigh the same number of pounds.

Present weight problem 3 (fig. 2.4) to the students. Unlike in the first two weight problems, in this problem the weight of one of the blocks is not given directly. The students have to decide which scale to consider first. The scale with two identical blocks is the best place to begin because, through guess and check or the recall of the addition of doubles, the students can find the weight of one sphere. Ask the following questions:

  • Which blocks are on scale A? (a sphere and a cube) How much do they weigh all together? (eleven pounds)
  • Do you know how much the sphere weighs? (No, we can't tell.)
  • Do you know how much the cube weighs? (No, we can't tell.)
  • Which blocks are on scale B? (two spheres)
  • How much do they weigh all together? (twelve pounds) 
  • Do you know how much each sphere weighs? (Yes, each weighs six pounds.)
  • How did you figure it out? (6 + 6 = 12, so half of 12 is 6.)
  • Can you figure out the weight of the cube? (yes)
  • How will you do that? (The sphere weighs 6 pounds, so the cube is 11 - 6, or five, pounds.)

 

Give the students copies of the "Block Pounds" activity sheet to do on their own or in pairs. Encourage the students to record the weights on the blocks as they are determined. Once the students have completed the problems, have them talk about how they solved them.

Note that the problems on "Block Pounds" are ordered by difficulty. Problem A gives the weight of one of the blocks directly. Problem B requires a knowledge of a doubles addition fact to find the weight of one block before the weight of the other can be computed. Problems C and D show three scales with three different types of blocks. In problem C, the weight of the sphere is given directly and the students have to replace the sphere on each of the other two scales with its weight to find the weights of the cylinder and cube. In problem D, no weight of a block is given directly.

 

 Student Assessment-

Show the children problem A from the student activity sheet and how it can be represented using addition equations (fig. 2.5). Say, "The equation for scale A says that the weight of the cube plus the weight of the cylinder is fourteen pounds. The equation for scale B says that the weight of the cube is five pounds. Let's talk about how you solved the problem. I will write the steps."

Call on the students to tell how they solved the problem. Encourage them to use the term replace in their discussion. Show them how to record the solution steps. For example:

Step 1: Scale B shows that the cube is 5 (pounds).
Step 2: Replace the cube with 5 in equation A. Then 5 + = 14.
Step 3: Find the weight of the cylinder by subtracting 5 from 14: 14 - 5 = 9.

So the cube weighs nine pounds.

Continue with "Block Pounds" problem B and record and discuss the steps. Have the students record the steps to the remaining two problems, C and D, on their own or in pairs.

Some students may count up from 5 to 14 to find the weight of the cylinder. Others may recall the addition fact 5 + 9 = 14. Still others may use subtraction or guess and check to find the missing addend.

All information obtained from NCTM:  Illuminations.  Lesson plan at:  http://illuminations.nctm.org/index_d.aspx?id=167#standard_top

 

----REFINEMENT- Prepared after the lesson and the post observation conference.

 

----IMPACT—Prepared after the lesson and post-observation conference

 Reflection/Analysis of Teaching and Learning-

Discuss student progress in relation to the sated objectives (i.e., what they learning with indicators of achievement.)  Discuss success of instruction as it relates to assessment of student progress.  Include three student samples (high, average, low) and an analysis of their performance based on assessment results.

 

----REFINEMENT—Prepared after the lesson and post-observation conference

 Lesson Extension/Follow up: 

Based on your reflection, discuss plans for subsequent lessons to reinforce and extend understanding particularly for students who did not make satisfactory progress.

 Note:  All three sections (ACTION,  IMPACT AND REFINEMENT) should be included in your portfolio for review by each committee member.