 Counting Back

• ## Counting Back

How Many More Fish?
Periods: 1
Author: Grace M. Burton

### Instructional Plan

Teacher Note: As you prepare to teach this unit, you may wish to consider what management strategy you will use to distribute the fish-shaped crackers. Packaging the fish-shaped crackers in resealable plastic bags, one for each student, will keep the materials sanitary. Bibliography of Books About Counting

To open this lesson, provide each student with crackers, two paper plates, crayons, and graph paper. Then read a counting book about fish (one option is Fish Eyes: A Book You Can Count On by Lois Ehlert) or some other counting book. If you do not have a book available, you may consider sharing a Fish Eyes read aloud. As the students listen to the story, have them model each number named by adding one fish-shaped cracker to a plate, writing that numeral at the beginning of a row on the graph paper, and then placing one fish cracker per square to show the number. [Encourage students to have rows of 10.] Then ask them to remove the fish, one row at a time; coloring the squares in that row that had held fish crackers. Have students color each row a different color using yellow, purple, and other colors of their choosing.

If you choose not to read a counting book, you might sing a favorite counting-up song, such as "This Old Man," and have the students model and record the number featured in each verse.

 1 2 3 4 5 6 7 8 9 10

To the tune of an easily-remembered song, such as "A Hundred Bottles of Beer on the Wall," sing a more appropriate counting back song, "Ten Little Fish on the Plate." Have the students place crackers on the appropriate bar on the graph they created in the activity above as they sing each verse of “Ten Little Fish.” [This activity allows you to determine whether any students have trouble matching numerals to sets, counting, or writing numerals.] Now ask: How many more squares are colored in the yellow bar than in the purple bar? How do you know? [Possible answer: 1; I counted one more. This question introduces the new mode of subtraction, the comparative mode.]

Next hold up a number, such as eight, and ask the students to put that many fish-shaped crackers on a plate and record the number of crackers. Then ask them to make a second plate with one less cracker.

Now tell them they will compare the number of crackers on each plate. To do this, have them remove pairs of crackers from the plates by taking one cracker in each hand from each of the plates and placing the crackers in the bag until crackers are left on only one plate. Then have them count the crackers left on the plate. Ask for a volunteer to model and record the comparison using the number sentence [equation or horizontal] format. [For example, 8 - 7 = 1.] Now ask for a volunteer to record the comparison using the vertical format. Encourage the students to describe the comparison in two ways, in one instance using the word "more" and in the other instance using the word "less." [For example, there is one more cracker on the plate that had eight crackers. There is one less cracker on the plate with seven crackers.] Adjustable Spinner

Ask a student to name a number from 5 to 10. Divide the spinner into that many parts. Now call on a volunteer to spin the spinner and tell which number came up. Ask the students to show the number with fish-shaped crackers. Then tell them to show a group of crackers that is one more than that number, and then a group that is one less. You may wish to have them record their responses on the One Less/One More Activity Sheet. One Less/One More Activity Sheet

Repeat with other volunteers.

To end the lesson, have the students divide some crackers between two plates, then remove a cracker from each plate until all the crackers on one plate are gone. [If you wish, you may encourage them to eat each pair of crackers as they remove it. If you prefer to use the crackers another day, be sure each bag is labeled with the student's name and closed securely.]

### Assessments and Extensions

Assessment Options

1. Students may draw plates that show "one more" and "one less" for entries for their portfolios.
2. The information that you collect about the students' understanding and skills throughout the unit allows you to focus on individual student's needs and strengths and plan additional learning opportunities. For this reason, a recording sheet, Class Notes, has been provided for you. You may also find the information that you record useful when discussing the students' progress.
Extension
Move on to the next lesson, How Many More?

### Questions and Reflections

Questions for Students

1. How many fish-shaped crackers are on this plate? (Show a plate with six crackers.) On this plate? (Show a plate with seven crackers.) Which plate has more? How many more? Which plate has less? How many less? How can you prove that?

[6; 7; the second plate has more; 1 more; the first plate has less; 1 less; student responses may vary.]

2. What number sentence would show that you compared a plate of six fish-shaped crackers with a plate holding five fish-shaped crackers?

[6 - 5 = 1.]

3. What is alike between the two ways that we recorded the comparisons? What is different?

[The same numbers are compared, but the way we wrote them was different (one way was horizontal, and one way was vertical.)]

4. How could you help a younger student find the answer to 7 - 6 by counting?

[Student responses may vary.]

5. What equation shows that you compared a plate of 8 fish-shaped crackers with a plate with 10 fish-shaped crackers?

[10 - 8 = 2.]

6. What does the minus sign mean?

[Subtract.]

7. What two symbols did you use to mean "equals"?

[In the equation form of recording subtraction, = is used. In the vertical form, the line symbolizes "equals."]

8. When you count backward, what comes after 10? After 7? After 1? What comes before 6? Before 4?

Teacher Reflection

• Were the students able to model the numbers as the books were read? What other books might I use?
• Which students were not yet able to record numbers of the bar graph?
• Which students met all the objectives of this lesson? What extension activities would be appropriate for those students?
• Which students did not meet the objectives of this lesson? What instructional experiences do they need next? What mathematical ideas need clarification?
• What adjustments will I make the next time that I teach this lesson?

### Objectives and Standards

Students will:
• Model numbers and write numerals to 10.
• Subtract from numbers to 10 by counting back.
• Record differences in vertical and horizontal format.
• Recognize the symbols used in recording subtraction.

Common Core State Standards – Mathematics

Pre K to 2nd

• Kindergarten
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.

Pre K to 2nd

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.

Pre K to 2nd

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.
Common Core State Standards – Practice
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP6
Attend to precision.

### Related Resources How Many More? Grade: PreK to 2ndWrite and modeling subtraction problems. Hopping Backward to Solve Problems Grade: PreK to 2ndUse a number line to determine differences. Balancing Equations Grade: PreK to 2ndUse a pan balance to model and write subtraction equations. Fact Family Fun Grade: PreK to 2ndRelate addition to subtraction with fish-shaped crackers. Wrapping Up the Unit Grade: PreK to 2ndAssess students' knowledge.