Section 2

Standards and Activities for Grade 4

Operations and Algebraic Thinking: 4.OA.1

“Use the four operations with whole numbers to solve problems.”

1. “Interpret a multiplication equation as a comparison, e.g., interpret as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.”

Background

Multiplication can be described as a comparison between the product and its factors. For example, means 2 groups of 8. It also means that 16 is 2 times as many as 8 or 8 times as many as 2.

Activity: Multiplication Tic-Tac-Toe Working in pairs or groups of three, students will complete tic-tac-toe boards by writing equivalent multiplication statements. The first person to get three equivalent statements in a row or along a diagonal wins. Materials Unlined paper for each student. Procedure 1. Explain that students will play multiplication tic-tac-toe, but note that this is a little different from the standard tic-tac-toe game. 2. Explain that prior to the game, each student will select a number from 2 to 50 as a product and write five equivalent multiplication statements about the product on a piece of paper. For example, suppose a student chooses the number 16. Some statements she could write are , , 8 groups of 2, 8 times as many as 2, or 4 times as many as 4. 3. Hand out the unlined paper. (If you are considering playing more than one round, you might have your students fold their papers in half from top to bottom. Using the front and back of the paper results in four regions, each of which can easily accommodate one tic-tac-toe board.) Instruct your students to draw a tic-tac-toe board as shown. Note that the boxes on the board should be large enough to accommodate multiplication statements. 4. Explain to your students that two students at a time are to play. The student who has the largest product goes first. She writes one of her multiplication statements in a box on the tic-tac-toe board. The other student then writes one of his multiplication statements. The first student to get three equivalent multiplication statements in a row or along a diagonal wins. Prior to declaring a winner, however, the other student must check that his opponent's multiplication statements are, in fact, correct. You may need to serve as referee in some instances. 5. Begin the games, following the procedure outlined above. 6. If time permits, play several rounds, with students selecting new products and writing new multiplication statements. Make sure that all students in groups of three have a chance to play. Closure Discuss the number of equivalent multiplication statements students generated. Choose a product, and on the board write as many equivalent multiplication statements as the class can generate.

Operations and Algebraic Thinking: 4.OA.2

“Use the four operations with whole numbers to solve problems.”

2. “Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.”

Background

Word problems can be efficiently solved if students follow these steps:

1. Read the problem carefully. 2. Understand the problem, recognize what information is provided, and what they are asked to find. (For example, phrases such as “how many times more” indicate a multiplicative comparison, and questions such as “how many more” indicate an additive comparison. Recognizing the differences between such comparisons can help students choose the correct operation to solve the problem.) 3. Develop a plan to solve the problem. Equations and diagrams are useful tools. If students write an equation, encourage them to use a symbol to represent the unknown quantity. 4. Follow the plan to solve the problem. 5. Check for accuracy and that the answer is reasonable. Activity: What's the Problem? Students are to draw a picture and then write a word problem based on the picture that can be solved using multiplication or division. They will then exchange their picture and problem with another student and solve each other's problems. Materials Drawing paper; crayons for each student. Procedure 1. For this activity, tell your students that they will use pictures as a starting point to write word problems that can be solved using multiplication or division. 2. As an example, suggest that students imagine a picture of 2 children and 4 cookies. Based on this picture, students might create the following problem: How many cookies could each child have if the cookies are shared equally? 3. Instruct your students to draw a picture in which groups having the same number per group must be combined (multiplied), or a total number of objects must be distributed equally (division). 4. Explain that after they have completed their picture, they are to write a word problem (based on their picture) that can be solved either by using multiplication or division. They should write their problem below their picture. 5. Instruct your students to exchange their picture and problem with those of another student. They are to write an equation with a symbol for an unknown number to represent the problem, and then solve the problem. 6. Remind students to read the problem carefully. Suggest that they use the picture to help them decide if the problem requires them to use multiplication or division to solve it. Closure Have volunteers present their pictures and problems to the class. Have the class solve some of the problems as a group. Select a few pictures that students used to write multiplication problems. Ask your students to provide a word problem, based on the picture, that can be solved using an additive comparison instead of multiplication. You may also want to display the pictures and problems.

Operations and Algebraic Thinking: 4.OA.3

“Use the four operations with whole numbers to solve problems.”

3. “Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.”

Background

Solving multistep word problems requires the same steps as solving simple word problems. Students must read the problem, understand the problem, plan how to solve it, carry out the plan, and check their answer.

Students must always be alert to the reasonableness of an answer. In division, sometimes remainders make no sense in the context of the problem. For example, consider a class of 26 students. If 6 students can sit at a table, how many tables must the classroom have? Simple division provides the quotient of 4 remainder 2. But if only 4 tables are provided, 2 students will not have seats. The reasonable answer is that 5 tables are needed.

Activity: Equations and Problems Working in small groups, students will solve multistep word problems. They will write an equation, using a letter to stand for an unknown quantity, solve the equation, and determine if the answer is reasonable in the context of the problem. Materials Scissors; one copy of the reproducible, “Problems and Reasonable Answers,” for the teacher's use. Preparation Make a copy of the reproducible and cut out the word problems along the broken lines. Procedure 1. Divide your class into eight groups and explain that they will be working with eight word problems. 2. Hand out a different word problem slip to each group. Explain to your students that after reading the problem and determining what they are to find, they are to write an equation that can be used to solve their problem, using a letter to represent what they are trying to find. After solving the problem, they are to determine if their answer is reasonable. Caution them to interpret quotients that have remainders, if necessary. Allow time for students to work. Explain that students should do all their work on a separate sheet of paper, not the slip of paper containing their problem. 3. After all groups have solved their first problem, instruct your students to exchange their problems with another group. For example, the group that had problem 1 should pass their problem to the group that had problem 2, and the group that had problem 2 should pass their problem to the group that had problem 3, and so on. (Note: Having groups working on one problem at a time allows you to manage the activity more efficiently and helps to keep the groups focused.) 4. Make sure that all groups have a chance to solve all eight problems. Closure Call on the final group that finished with problem 1 and ask them to present their work to the...