MA.4.NSo.1.5 – Plot, order, and compare decimals up to the hundredths.
OBJECTIVE: Students will learn and understand how to compare decimals up to the hundredths place.
MATERIALS: (Per Group of 2)
1 regular deck of playing cards
2 Decimal Game boards
LESSON DISCUSSION:
• Define the term decimal and review the decimal place values of numbers up to tenths and hundredths.
• Review the place values of numbers involving decimals. Make sure students understand that for place values involving decimals, the closer a digit is to the decimal point, the greater the value. For example, the decimal 0.01 is less than 0.1, since the 1 in 0.1 is closer to the decimal point. It has a greater place value than the 1 in 0.01.
Part a:
Teacher Preparation:
Remove all the face cards (kings, queens, jacks, and jokers) and the “10” cards from the decks.
Procedure:
Step 1: Separate the class into pairs. Inform the students that the ace cards have a value of 1.
Step 2: Instruct the pairs to sit side by side with their Decimal Game boards in front of them.
Step 3: Student pairs shuffle their deck and split the cards equally between the 2 of them. Tell them to keep their stacks face down once all the cards have been distributed.
Step 4: Instruct each player to draw the top 2 cards from their stacks, placing them face up on their Decimal Game board. Students arrange the cards they drew to make the largest number possible. The 2 cards will form a decimal number.
Step 5: Have the students compare their 2 decimal numbers. The player with the greater decimal number gets to claim all 4 cards for the round and place them in their separate “win” pile.
Step 6: Students continue dealing and claiming cards until all the cards have been drawn. Note that the students’ last deal will only have 1 card.
Step 7: The player who collects the greatest number of cards wins.
Step 8: Have the students repeat the activity with a different partner.
Extension Activity
Repeat the entire activity, but this time the students draw 3 cards at a time. The third card is placed over the zero to represent the whole.
Part b:
MATERIALS: (Per group of 4)
1 regular deck of playing cards
4 Decimal Game boards
1 Number Line printout
1 Write and Wipe holder
1 dry erase marker
1 dry eraser
Teacher Preparation:
Step 1: Place a Number Line printout in a Write and Wipe holder for each group.
Step 2: Remove the 10’s, jokers, jacks, queens, and kings from each deck of playing cards. Explain to the students that the ace card represents 1.
Step 3: Distribute the materials to each group.
LESSON DISCUSSION:
• Discuss how the marks on a number line can represent both fractions and decimals.
• Review that tenths on a number line are represented by ten equal “jumps” between whole numbers.
PROCEDURE:
Step 1: Separate the class into groups of 4.
Step 2: Instruct the students to sit side by side with their Decimal Game boards in front of them.
Step 3: Have the groups shuffle their decks of cards, splitting them equally between each member of the group. They should keep their stacks face down once all the cards have been distributed.
Step 4: Instruct each player to draw the top 3 cards from their stacks, placing them face up on the Decimal Game board. Students arrange the cards they drew to make the largest number possible. The third card is placed over the zero to represent the whole.
Step 5: Have the students compare their decimal numbers, carefully rearranging their Decimal Game boards so they are in ascending order.
Step 6: Have students work together to plot their individual decimals on the Number Line printout. Confirm accuracy.
Step 7: Students will then discard their cards, erase the plots on the number line, and repeat steps 2 through 6 until their cards have run out.
Essential Questions for Discussion or Journaling:
(1) Explain the process of comparing decimals.
(2) How can a number line help us visualize decimals?
Place card with the highest value here.
Place card with the lowest value here.
DECIMAL GAME BOARD
Number Line
LEVELED PRACTICE 1 – MA.4.NSO.1.5
DIRECTIONS: Shade in the models and use >, <, and = symbols to compare the decimals below.
Explain how you can compare the decimals 1.45 and 0.54 without looking at the decimal portion of the numbers.
DIRECTIONS: Plot the decimals given on the number lines and compare them using the symbols >, <, or = .
Which decimal from the set {0, 0.4, 0.8, 0.95} is closest to 1/2? Use a number line to help you determine your answer.
Name: ___________________________________________
LEVELED PRACTICE 3 – MA.4.NSO.1.5
DIRECTIONS: Find decimals that match the given scenarios.
1 2 3 4
Lisa wants to find decimals that are greater than 0.75 but less than 0.85. Give 3 examples of decimals that Lisa could use.
Stephanie is trying to guess the decimal Manny is thinking of. She knows his decimal is less than 0.55 but more than 0.5. Give 3 decimals that Stephanie could guess.
Leon is trying to find the perfect amount of flour he should use for his recipe. He wants to test baking with 3 different amounts that are greater than 0.65 teaspoon but less than 1.5 teaspoons. Give 3 decimal amounts that Leon can try.
Ricardo wants to find all the decimals to the tenths place that are greater than 0.5 but less than 1.5. Help Ricardo find all the decimals.
Place the decimals 0.45, 0.6, 0.84, and 0.64 in ascending order.
MA.4.NSO.2.4 – Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as a fractional part of the divisor
MA.4.NSO.2.1– Recall multiplication facts with factors up to 12 and related division facts with automaticity.
OBJECTIVE: Students will practice division of whole numbers of up to fourdigit dividends and one-digit divisors.
MATERIALS: (Per teacher)
1 classroom dry erase board
1 dry erase marker
1 dry eraser
MATERIALS: (Per Student)
1 egg carton (4 egg holders)
1 dry erase board
1 dry erase marker
1 dry eraser
1 Egg Tray Division worksheet
75 counters
Teacher Preparation:
Cut each egg carton into two horizontal strips of 4. Only two strips will be cut from each egg carton, and the rest can be recycled. Each student will get one of the halves of the egg carton.
LESSON DISCUSSION:
• Review place value. Remind the students that 10 ones is equal to 1 ten, 10 tens is equal to 1 hundred, and 10 hundreds is equal to 1 thousand.
• Discuss the properties of multiplication and how they are related to division.
• Identify the meaning of dividend, divisor, and quotient when dividing.
Part A:
Procedure:
Step 1: Tell the students to place their egg holder on the dry erase board. Have them draw a horizontal line above the holder and a vertical line on the left, perpendicular to the horizontal line.
Step 2: Write the division problem 6,429 ÷ 4 on the classroom dry erase board.
Step 3: Ask the students to set up the egg holder to be the four-digit dividend by adding the number of counters indicated by the digit to each egg holder. There should be 6 counters in the far left cup, 4 in the cup to its right, 2 in the third cup, and 9 in the last cup.
Step 4: Have students write the number 4 as the divisor on the left side of the vertical line.
Step 5: Explain that groups of 4 must be removed from the first cup as it is the divisor. Students will divide 6 by 4. Have students remove as many sets of 4 counters as possible, writing the number of sets removed on the horizontal line above the thousands place. The students should write 1. Those counters can be set aside.
Step 6: Point out that there are 2 counters remaining in the first cup, so another group of 4 cannot be removed.
Step 7: Explain that the 2 counters remaining in the first cup combine with the 4 counters in the second cup to further divide the number. The 2 counters now represent 2 tens or 20. Have students add counters until there are 20 in the first cup. The 4 counters in the second cup represent 4 ones. Students will now try to find how many times 4 divides into 24.
Step 8: Have students remove as many sets of 4 as possible from 24, counting how many sets of 4 were removed. This number of sets removed are written on the line over the hundreds place. They should write 6, and there should be no counters left in the first or second cup.
Step 9: Ask students to determine how many groups of 4 can be removed from the 2 in the third cup. Help students understand that zero groups of 4 can be removed from the third cup, and they should write the digit 0 on the horizontal line above the tens place.
Step 10: Explain that the 2 counters remaining in the third cup combine with the 9 in the fourth cup to divide the number further. The 2 counters now represent 2 tens or 20. Have students add counters until there are 20 in the third cup. The 9 counters in the fourth cup will represent 9 ones. Students will now try to find how many times 4 divides into 29.
Step 11: Repeat step 8. Students find how many sets of 4 are in 29 by removing sets of 4. The number written above the ones place is 7. There should be 1 counter left in the ones place, which represents the remainder.
Step 12: Discuss what the remainder of 1 means. Students must be able to express a remainder as a fraction. In this case, we have 1 out of 4 (the divisor) counters in a group left over. 1 out of 4 can be represented as 1/4, so the answer is 1,607 1/4.
Step 13: Clear the trays and repeat the steps using the next problem from the Egg Tray Division worksheet until all the problems have been solved.
Extension Activity
Step 1: Have the students practice division without the use of the egg tray by dividing a 3-digit number by a 1-digit number.
Step 2: Have the students practice division without the use of the egg tray by dividing a 4-digit number by a 1-digit number.
Part B:
OBJECTIVE: Students will work towards mastery of multiplication and division facts.
MATERIALS:
MATERIALS: (Per group of 2)
2 plastic cups
26 craft sticks
1 dry erase board
2 dry erase markers
1 dry eraser
2 Division printouts
2 Write and Wipe holders
LESSON DISCUSSION:
• Discuss the importance of mastering multiplication and division facts within 12. Share ways that these facts are used in fourth grade and beyond.
• Explain the relationship between multiplication and division. Use fact families as a way to help students make this connection.
Teacher Preparation
Step 1: For each group of two, number two sets of craft sticks 0 - 12. Each stick should have the number written towards the bottom so that it is not visible when placed in a cup.
Step 2: Separate the sticks into two cups, with 0 - 12 in each set.
Step 3: Print out two Division printouts, placing them inside the Write and Wipe holders.
Procedures:
Step 1: Pass out all the materials, making sure the numbers on the sticks are facing down in the cup.
Step 2: Student A pulls one stick from each cup, using the numbers to write a multiplication equation on their dry erase board: ____ x ____ = ____. Student B solves the equation and writes the answer in the last blank.
Step 3: Students return the sticks to the original cups.
Step 4: Repeat steps 1 through 3, swapping roles until students grasp the concept of multiplication.
Step 5: Ask the students to pull out their Division printouts.
Step 6: Each partner will use a cup of sticks (with sticks 0 - 12) for this activity. Simultaneously, partners each pull a random stick from their cups and use them to complete their printout by writing their numbers in the middle blank all the way down the page, completing the left column as quickly as they can.
Step 7: When both partners are done, they swap pages and check each other’s work. For each correct answer, they earn a point. If they were the first partner finished, they add an additional two points. Students keep track of points for Round 1 on their dry erase board.
Step 8: Students should place their sticks back in their own cup, making sure they have numbers 0 - 12. All numbers should be placed number-side down.
Step 9: Repeat steps 1 through 4 for 3 more rounds. The student with the most points at the end of 4 rounds is the winner.
Extension Activity
Step 1: Randomly assign each student two numbers between 1 - 12.
Step 2: On their dry erase board, each student creates a multiplication and division fact family for those numbers, writing 4 equations to represent their relationship.
Step 3: Partners or neighbors check each other’s work.
Step 4: Repeat, if desired.
Essential Questions for Discussion or Journaling:
(1) How does the process of egg tray division represent long division?
(2) How are multiplication and division related?
(3) Why is it important to build fluency of multiplication and division facts?
DIRECTIONS: Solve the division problems below using a strategy of your choice. Be sure to show your work. Express remainders as fractions of divisors.
DIRECTIONS: Solve.
DIRECTIONS: Draw a model to represent each equation below and solve.
LEVELED PRACTICE 3 – MA.4.NSO.2.4
DIRECTIONS: Select all the expressions that have a quotient equivalent to the one given.
Quotient: 25
Quotient:
Quotient:
Write and solve a division problem using a 4-digit dividend and a divisor of 7 that results in a quotient with a remainder of 5/7. Show your work.
MA.4.DP.1.3 – Solve real-world problems involving numerical data.
OBJECTIVE: Students will solve real-world problems by analyzing data and graphs.
MATERIALS: (Per Group of 6)
1 data template and accompanying questions
1 Write and Wipe holder
1 dry eraser board
1 dry erase marker
1 dry eraser
LESSON DISCUSSION:
• Review ways that data can be shared, specifically in a table, stem-andleaf plot, and line plot.
• Review how to create a data table, line plot, and stem-and-leaf plot.
• Discuss the importance of analyzing a graph before answering questions about it. For example, what do the X marks or stems and leaves represent? Is there a key available to help us better understand the graph? What unit and scale are used?
Teacher Procedure:
Print out and place a data template and accompanying questions in a Write and Wipe holder for each group of 6 students.
Procedure:
Step 1: Divide the class into 4 groups. Give each group one data template and the accompanying questions. Explain to the students that they are responsible for completing their own data collection for their template, creating their graph, and sharing their findings to the class.
Step 2: Assign one person in each group the task of data collector. This student moves around to the other 3 groups to gather answers to their group’s specific question on the dry erase board. The other members of each group stay in place and share their answers to each of the other data collectors. Once they have gathered answers from all the other groups, the data collectors return to their groups.
Step 3: Each group will use the data collected to create the plot assigned to them on their template. They should take time to consider scale, title, units, key, and other elements if applicable to their plot.
Step 4: Once complete, students work together to answer their accompanying questions.
Step 5: If time allows, students share their plots and observations about their data to the class.
Extension Activity
Step 1: Using their group’s completed plot, students write 3 - 5 additional questions based on their data.
Step 2: Groups rotate and answer these additional questions with at least one other group’s data and then check their answers with that group.
Step 3: Rotations can repeat until all groups have been visited.
Essential Question for Discussion and/or Journaling:
When answering questions about a table or graph, what details must we look at to understand the information?
Directions: Survey the students in your class to see how many siblings each one has. Record the data in the table below. Create a line plot to represent the data and answer the questions on the back.
Group 1: Number of Siblings
Group 4: favorite color
Directions: Answer the following questions about the data gathered.
1. Which color was chosen most in the class?
2. How many more students chose that color than the least chosen color?
3. How many students had a favorite color that was not specifically listed?
4. How many students prefer green?
5. How many students chose blue, red, or yellow?
LEVELED PRACTICE 1 – MA.4.DP.1.3
DIRECTIONS: The line plot below shows different heights of pipes. Use the information from the line plot to answer the questions.
How many 1/4 - meter pipes are there?
How many 3/4 - meter pipes are there?
What length of pipe is the most common?
How many more 2/4 - meter pipes are there than 3/4 - meter pipes?
Why is it important to take note of a graph’s title, units, scale, and key before analyzing the data?
DIRECTIONS: Use the data presented in the table below to answer the questions.
What was the most common number of books read last month by the fourth grade students?
How many students read at least 2 books last month?
How many students were surveyed?
What is the difference between the number of students that read 1 book and the number of students that read 3 books?
Which would be the easiest way to display the data above: a line plot, a stem-and -leaf plot, or bar graph? Why?
LEVELED PRACTICE 3 – MA.4.DP.1.3
DIRECTIONS: Annette recorded the amount of time it took her to get to work every day for 5 days. It took her a total of 61.5 minutes to get to work and the commute times were not always the same. Create a stem-and-leaf plot using the template below to show how long it may have taken her to go to work each day last week.
Key: =
Determine a different data set that could be used to answer the question above.
