Activity Name: Hit the Target



Activity Name: The Target Game Grade level(s): 5-7

Skills/Goals: Students will use multiplication to arrive at an answer within a given range of values. Each time the game is played, the range is narrowed. The activity helps students develop a number sense of multiplying by decimal numbers. The role of place value becomes evident as the activity progresses. The activity can then be altered to use division in place of multiplication.

Assessment Anchor(s) & Eligible Content addressed:

M05.A-T.1.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left.

M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).

M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing).

M06.A-N.2.1.1 Solve problems involving operations (+, –, ×, ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.

M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

Students: whole class activity

Materials needed:

An overhead calculator or a computer generated calculator that can be visible to the entire class at the same time, a place to write problems (and the answer) created by the students, usually in the form 66 x 2.3 = 151.8 or 1024.6 / .93 = 1101.7204

Directions:

• The students should not have any paper, pencil, or calculator. The only calculator should be the one the whole class sees. You want them to focus on the work being done by the whole group.

• A student will be needed to record the problems and their answers on a board visible to all students. It might be best to write the problems horizontally in a vertical list, with a succeeding problem below the previous one. This way, students can follow the progression of the activity.

• Begin by defining a target range, depending on the level of the students, the range can be anywhere between two and five hundred. For example, a starting range could be 2,700-3,000. The round is finished when the answer to the multiplication problem falls within the target range.

• Explain to the students that they will only be permitted to use multiplication to arrive at an answer within the target range. Students will go in turn until everyone has had a chance to propose a problem with a result that they hope will fall in the target range.

• Chose a starting number, it should be something that is not easily multiplied by a number to get a product within the target range. I usually start with 66, since my first car was a 1966 Buick. Enter the starting number in the calculator.

• Ask the first student to pick a number to multiply by the starting number in the hopes that the product will be within the target range. Whatever number the student chooses, multiply it by the number shown on the calculator. The student recording will need to write the starting number and the number the student picks to multiply it by on the board. When the product is shown, the recorder writes it in the problem. If the student picks 40 as the multiplier, I suggest writing the problems in the form 66 x 40 = 2,640.

• The purpose of the recorder is twofold. First, it allows students to see what multipliers they have chosen and to see what result they have produced. This will come in very handy as the game progresses. Second, it provides a record in case of a calculator malfunction. You can always go back and reenter the values.

• The next student now starts with the product from the previous problem. In the above example, he or she would have to multiply 2,640 by some number to get a product within the target range. This is where students begin to develop an understanding of multiplying by decimal numbers. They will eventually need to multiply by numbers like, 1.03, 1.01, 1.001, .9, .95, .99 and so on. The closer they get to the target range, the closer their multiplier will be to one.

• Continue to record all problems so students can see which values make the product larger and which values make it smaller. You may need to assist them in looking at the problems to see what is happening when they choose certain multipliers.

• Don’t be surprised if they come up with a product that is greater than the target range and assume they have lost the game, that it is not possible to get a smaller value by multiplying. It may also be the case that they suggest using negative numbers to make the product smaller. You will find out much about their number sense with regards to multiplication of decimals.

• The round continues until the product is within the target range. Don’t be surprised if it takes many tries. I have had rounds where each student has had a chance to play and we have not landed in the target range. I simply started back with the first student, and continued until the result was in the target range.

• Whenever you finish the round, you can begin another. I usually shorten the target range each time we play and chose a different starting number. The smaller the target range, the more students need to know about multiplying decimal number in order to get a product within it. They will begin to multiply by numbers with two, three, and maybe four decimal places. They begin to realize the size of those numbers with relation to each other and to one, and the affects they have on finding a product within the target range.

• Students can look at the recorded problems to help them draw some conclusions about multiplying by decimal numbers.

• Eventually, students will conclude that multiplying by a number greater than one makes the product larger, and multiplying by a number smaller than one makes the product smaller. The closer the number is to one, the less the change in the product.

• Hopefully, you will find the students getting better at choosing their numbers and that the rounds take less and less time to complete. The students are developing a sense of multiplying decimal numbers.

• If students are having a great deal of difficulty, it may mean the target range you chose was too small. You will need to use your sense of what your students understand to guide you in that manner. I usually use target ranges of, 500, 400, 300, 200, 100, 50, 25, 20, 10, 5, and 1.

Extensions:

• The last time you play the game with multiplication, the range can be one, such as 1,456-1,457. This can be a real challenge, but one the students will take great pride in accomplishing.

• After the students have become very familiar with the game played using multiplication, now change the operation to division. They can then investigate the role of decimal numbers and place value with relation to division.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download