Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (25 page)

The prime numbers that are less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. (1 is neither prime nor composite.) All other numbers that are less than 100 are composite numbers.

Activity: The Prime Challenge

Working in small groups, students will play the game “The Prime Challenge,” in which they will identify prime and composite numbers.

Materials

Pens; one 4-inch-by-6-inch index card for each group of students; a dark marker for the teacher.

Preparation

Make a number card to easily identify groups. Fold the index cards in half, resembling a tent. Use a marker to label each card with Group 1, Group 2, and so on until each group has a number. On a sheet of paper, make a score sheet with group numbers labeled in each column, as shown below. (
Note:
You may have more than six groups.)

Procedure

1.
Distribute the group number cards, one to each group. Students should place the card on their desk so that you can easily see the group number to facilitate scoring.

2.
Ask each group of students to use a pen to write any 10 numbers between 1 and 100 on a sheet of paper. (
Note:
Using a pen prevents students from changing their numbers.)

3.
Instruct each group to circle the prime numbers from the numbers they wrote. When called upon, they will read the prime numbers they circled.

4.
Explain the rules. You will call on one group at a time. A group member will read the first prime number that the group circled. The other groups must agree or disagree if the number is a prime number. If a group disagrees, it must show a correct pair of factors. Following is an example of the scoring process, using Group 1:

• If Group 1 is correct, and the other groups agree, Group 1 gets 10 points.
  
• If Group 1 is correct, but a group feels that Group 1 is incorrect, the other group must offer a pair of factors to show why the number is not prime. If the first disagreeing group is incorrect, they lose 10 points. Likewise, if another group disagrees and is incorrect, they also lose 10 points. Group 1 gets 10 points.
  
• If Group 1 is incorrect, the first group to disagree and state a correct pair of factors gains 10 points. Group 1 then loses 10 points.
  
• If Group 1 is incorrect and no other groups disagree, or if disagreeing groups cannot provide a correct pair of factors, you provide the factors and all groups lose 10 points.
  

5.
Offer this example: Suppose Group 1 said 29, and no other group disagreed. Group 1 gets 10 points. If Group 1 said 29 and another group disagrees, Group 1 gets 10 points for being correct. The group that disagreed loses 10 points. If Group 1 said 12 is prime, which is incorrect, the first team to disagree and show a correct pair of factors gains 10 points. Group 1 also loses 10 points. If Group 1 said 12 is prime and no other group disagrees, all teams lose 10 points.

6.
Begin the competition with Group 1. Ask them to read the first prime number they circled. Ask if the class agrees. If there is disagreement, call on the first group that disagrees. If the disagreeing group presents incorrect factors, call on the next group that disagrees to present correct factors. Once correct factors are presented, award points and mark them on your score sheet.

7.
Now go to Group 2 and ask them to state the first prime number they circled. Follow the same procedure, and then move on to the other groups.

8.
After all the groups have stated their first prime number and all points have been awarded, return to Group 1 and ask them to state their second prime number. In instances where the prime number a group has circled has already been used, simply have them move on to their next circled prime. If a group uses all of their prime numbers and the game is not finished, they can still participate by agreeing or disagreeing with the other groups.

9.
Continue the procedure until all prime numbers have been read.

Closure

Tally the scores and declare a winner. Do a special bonus round. Present at least three composite numbers, one at time, from 1 through 100. Ask the groups to list all of the one-digit numbers (other than 1) that the composite number is a multiple of. For example, 35 is a multiple of 5 and 7; 64 is a multiple of 2, 4, and 8. (
Note:
64 is also a multiple of 16 and 32, but 16 and 32 are not one-digit numbers and should not be listed.) Present a number and have groups write their answer on a sheet of paper, and then turn their paper face down. Ask each group one at a time to reveal the answers they wrote on their paper. Groups receive one point for naming each one-digit number of which a composite number is a multiple. For instance, for 35, if students name 5 and 7, they receive two points. For 64, if they only name 2 and 8, they receive two points. For each incorrect number, they lose a point.

Operations and Algebraic Thinking: 4.OA.5

“Generate and analyze patterns.”

5. “Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.”

Background

A hundreds chart is a useful tool that can be used to generate a variety of numbers. These numbers depend upon the starting number and the number that is added to it.

The patterns that can be generated can surprise students. For example, sometimes a pattern will generate only even numbers. Starting with 2 and adding 2 results in a pattern of 2, 4, 6, 8, … Sometimes a pattern will generate only odd numbers. Starting with 1 and adding 6 results in 1, 7, 13, 19, … And sometimes a pattern will generate even and odd numbers. Starting with 2 and adding 3 results in a pattern of 2, 5, 8, 11, …

Activity: Number Generator

Working individually or in pairs, students will virtually create and identify numbers on a hundreds chart.

Materials

Computers with Internet access for students; computer with Internet access and digital projector for the teacher.

Procedure

1.
Explain that students will generate number patterns on a hundreds chart. A hundreds chart is a list of numbers ranging from 1 to 100 arranged on a 10-by-10 grid.

2.
Instruct students to go to
http://nlvm.usu.edu
. They should click in the grades “3–5” column on the “Number and Operations” row and then scroll down and click on “Hundreds Chart.”

3.
Once students have the hundreds chart on their screens, explain that at the top of the chart is “Count By” and “Starting At.” Students can decide what number to start at by using the up or down arrow. To decide what number to count by, they can also use the up or down arrow. After they have decided on their numbers, they should click on “Practice” at the bottom of the grid. (
Note:
This might already be selected.)

4.
Explain that students should now click on the number they chose to start with, and then click on the next number that they chose to count by. For example, if a student decided to start with 4 and count by 3, she would click on 4, 7, 10, 13, 16, … Correct numbers in a pattern will be colored blue; incorrect numbers will be colored red.

5.
Ask your students to explain the pattern. (
Note:
Clicking on “Show” will show the pattern up to 100 and clicking on “Animate” will show the progression of the pattern.)

6.
Instruct your students to click on “Clear” to clear the grid and start the procedure again.

7.
Allow time for your students to explore various patterns. Students should record some of the patterns they explore so that they may share them during the closure.

Closure

Ask your students to explain the patterns they found. Ask volunteers to suggest other numbers to start with and count by. Input this data on the hundreds chart and click on “Animate” to generate the pattern. Discuss the patterns.

Number and Operations in Base Ten: 4.NBT.1

“Generalize place value understanding for multi-digit whole numbers.”

1. “Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.”

Background

The value of a digit depends on its place in a number. For example, the value of 9 in 94 is 90; the value of 9 in 937 is 900. The value of a digit in one place is ten times the value of the digit in the place to its right.

Activity: Making Models of Place Value

Students will work in groups to create a place-value model, showing values in the ones, tens, and hundreds places. The class will then create a place-value model showing values in the one, tens, hundreds, and thousands places.

Materials

Scissors; glue sticks; four copies of reproducible, “Picture Pencils,” for each group of students. Optional: Card stock; masking tape or mounting tape for the teacher.

Preparation

To create the class place-value model, you will need an area of about 15 square feet, or about three feet by five feet. You may use the board, your classroom floor, a wall in a hallway, or a similar flat surface.