Wednesday, September 21, 2016

Vanessa Paganelli- A Remainder of One Book Club Post





Title:  A Remainder of One
Posted By: Vanessa Paganelli
Author: Elinor J. Pinczes
Illustrator: Bonnie Mackain
Recommended Grade Levels: Grades 2-4 
( When students are introduced to odd/ even numbers, division & remainders)






CCSSM Standards:
2nd grade:
Grade 2, Operations & Algebraic Thinking
  •     CCSS.Math.Content.2.OA.C.3
       Determine whether a group of objects (up to 20) has an odd or even number of              members, e.g., by pairing objects or counting them by 2s; write an equation to 
express an even number as a sum of two equal addends.
3rd grade:
Grade 3, Operations & Algebraic Thinking
CCSS.Math.Content.3.OA.A.2
   Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Grade 3, Operations & Algebraic Thinking
CCSS.Math.Content.3.OA.A.3
           Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Grade 3, Operations & Algebraic Thinking
CCSS.Math.Content.3.OA.C.7
   Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

4th Grade: 
Grade 4, Operations & Algebraic Thinking
CCSS.Math.Content.4.OA.A.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.

Summary: The story ‘ A Remainder of One’ introduces readers to Joe, an ant who is always the cause of an uneven line. Joe is left the remainder of the bugs because he is the 25th bug, which is an uneven number. Joe becomes frustrated throughout the story as he keeps finding himself standing aside of the line and making all of the lines uneven. He studies the problem and is determined to make the queen who loves even lines happy. He rearranges the twenty five (odd numbered bugs) in his squadron from two to three to four lines. He finally realizes that his resolution should be five lines of five bugs and Joe fits in at last and the queen is happy! This books vibrant and detailed illustrations and rhyming theme keep readers engaged and intrigued all  while learning mathematical strategies and vocabulary through literacy. The array of difficulty ranges which is great because this story can be used widespread across different grade levels and differentiated academic levels.
     
Rating 5 stars!
This story gets a five star rating because it  does a great job of teaching the readers how some mathematical problems take many different strategies and “try’s” to work out. It also shows that brainstorming and trying different strategies helps people (Joe) to figure out the best solution to his problem. This story encourages readers to try and try again. This story also introduces many different mathematical topics such as odd and even numbers, division and remainders. This story is engaging and keeps the reader intrigued and wondering what Joe may do next! The language in this book is advanced and gets readers to not only adventure into math but also keeps the literacy practice throughout its entirety. By using vocabulary such as “squadron” and “remainder” and “infantry”, “hovered”and “divine”, children are able to be introduced to math vocabulary and key terms in literacy that advance their vocabulary skills and introduce them to advanced academic language for both subjects.

Classroom Ideas:
2nd Grade: 

Introduce difficult vocabulary beforehand. Read the story on the rug as a read aloud. Allow students to question and make predictions in partnerships on how to solve Joe’s problems throughout the story. Have students use manipulatives such as small plastic bugs or small cubes and have a worksheet with different odd and even numbers. Teach students definition of odd and even numbers. 

Model what the children will be doing. Model Finding a number such as (8) and if each bug had a bug buddy that makes a pair which means that is an even number, but if there is a bug that is leftover, that is considered an odd numbers because it does not have equal pairs. Explain this thoroughly. Have students work in pairs. Walk around classroom assisting students who may need extra help or further instruction.

3rd Grade: 

Introduce difficult vocabulary beforehand. Read the story on the rug as a read aloud. Allow students to question and make predictions in partnerships on how to solve Joe’s problems throughout the story. Have students  work individually as you reread the book and use manipulatives, such as small plastic bugs or small cubes and recreate the different lines of bug squadrons as the book. 

Make sure that all students are correctly modeling the formations. Arrange students in groups of four, After completing the activity, collect all "bugs" from students. Students will be arranged into groups of four or so. Students can choose another math manipulative (cubes, coins, etc.)Students in the group decide on a number between 20 and 50 and select that many of the manipulative. 

Students will work together to find different ways to use their chosen manipulative to create marching groups just like Joe.Students will then record and share their findings with other students. They are learning different strategies from one another will using math tools strategically.

4th Grade:

Introduce difficult vocabulary beforehand. Read the story on the rug as a read aloud. Allow students to question and make predictions in partnerships on how to solve Joe’s problems throughout the story. Each time that Joe thinks of a new way to arrange his squadrons, the students will try the arrangement with counters. Each student will get 25 counters. They will have 24 of the same color and one in a different color to represent soldier Joe. Students can work in pairs or individually. When the troops arrange in two lines, have students divide their 25 counters into two rows with equal rows. Discuss as a class and explain that there was an odd number of counters, which is why it did not divide equally.

Explain that the remainder is important and needs to be accounted for in the equation. Write : 25 ÷ 2= 12 R 1 on the board. (explain how Joe is the remainder)
Use different colors of chalk or markers to circle the dividend (25), divisor (2), quotient (12), and remainder (1) and to label what they represent. As you are circling each part of the division equation explain that the dividend is the number being divided, the divisor is the number that you divide by, the quotient is the answer after you divide one number by another, and the remainder is the amount left over after a division.  

Continue reading the book. Each time the squadron rearranges themselves, have the students use their counters to explore what is happening in the book. The squadron arranges itself into three lines and then into four lines. Ask students to write the equations in their notebooks. Introduce various ways of writing a division problem on the board.
 
Have students wonder how they could solve this problem by using their multiplication facts instead of counters? Ask students to think of the facts that include 3. Ask, "Is there a number you can multiply by 3 to get 25?" [No.] "How close can you get?" [24.] 
When you have finished rereading the book, ask students to take 1 - 5 additional counters. Explain that this is their new squadron. Give each student a few random playing cards and worksheet.


Have students share their division illustrations and equations. Division is dividing equally among groups. If there is not enough to go into each group, then the answer has a remainder. Have students label new vocabulary and explore new understandings and strategies independently and then share.

1 comment:

  1. Vanessa,
    I really like that you picked a book that can be used across grade levels. It is great to find a book like this to add to our future libraries as future teachers. As teachers we sometimes change grades that we teach. I love that if we purchased this book, and are moved, we can still use this book to teach lessons! Additionally, I LOVE the activities at each level. This sounds like a great book to promote mathematical thinking in our students! It would definitely be worth the investment! Thank you for sharing!

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