K.1.2 Operations

NCTM Illuminations

• Five Frame

Thinking about numbers using frames of 5 can be a helpful way to learn basic number facts.  The four games that can be played with this applet help to develop counting and addition skills. 

• Ten Frame

Thinking about numbers using frames of 10 can be a helpful way to learn basic number facts.  The four games that can be played with this applet help to develop counting and addition skills. 

• Let's Count To 10:   

• Lesson 1 - Building Numbers to Five:  
  • In this lesson, students make groups of zero to 5 objects, connect number names to the groups, compose and decompose numbers, and use numerals to record the size of a group.  Visual, auditory, and kinesthetic activities are used to help students begin to acquire a sense of number.
• Lesson 2 - Writing Numerals to Five:  
  • As students construct groups of a given size, recognize the number in the group, and record that number in numerals, they learn the number words through 5 in order (namely, to rote count), and develop the ability to count rationally.
•  Lesson 3 - Building Sets of Six:  
  • In this lesson, students construct sets of six, compare them with sets of a size up to six objects, and write the numeral 6.  They also show a set of six on a "10" Frame and on a recording chart.
• Lesson 4 - Building Sets of Seven:  
  • Students construct and identify sets of seven objects.  They compare sets of up to seven items, and record a set of seven in chart form.
• Lesson 5 - Building Sets of Eight:
  • Students explore the number 8.  They make and decompose sets of eight, write the numeral 8, and compare sets of up to eight objects.
•  Lesson 6 - Building Sets of Nine:  
  • Students construct sets of up to nine items, write the numeral 9, and record nine on a chart.  They also play a game that requires identifying sets of up to nine objects.
•  Lesson 7 - Building Sets of Ten: 
  • Students explore sets of up to 10 items and practice writing the numbers 0 through 10.  Students count back from 10, identify sets of up to 10 objects, and record 10 on a chart.  They also construct and decompose sets of up to 10 items.
•  Lesson 8 - Wrapping Up the Unit: 
  • Students review this unit by creating, decomposing, and comparing sets of zero to 10 objects and by writing the cardinal number for each set.

• Let's Count to 20: 

In this unit, students make groups of 10 to 20 objects, connect number names to the groups, use place value concepts, compose and decompose numbers, and use numerals to record the size of a group.  Visual, auditory, and kinesthetic activities are included in each lesson.  This unit is most appropriate for students typically in the first grade.  

Other Instructional Activities

Composing and Decomposing Numbers

• Fingers

Kindergartners combine the number of fingers on two hands.  Click on the hands in the menu bar and set the viewing timer to five seconds as you begin play. 

• Beads

Beads are displayed for a few seconds, students click to tell how many beads they saw. Click on the beads in the menu bar and set the viewing timer to five seconds. 

• Flash fingers, dice or a ten frame to students and have them answer questions like: What did you see?  How did you see it?  How many are there altogether?  The flash time is adjustable.

Finger Patterns

• Partitioning Numbers 3 to 10: Place your hands on your head. Make 3 on your fingers.  Can you make three another way?  Check to see if you are correct.  Make 4 on your fingers. How many ways can you make 4? Similarly for 5, 6, ...10
• Partitioning 10 fingers: Put your hands out in front.  Show me 10 fingers.  Put down one finger.  How many does that leave?  What does 9 and 1 make?  Do the same with 8 and 2; 7 and 3; so on.

Wright, R., Martland, J., Stafford, A., & Stanger, G. (2007). Teaching number (2nd Ed.) Sage Publishing, 2007.

Additional Instructional Resources

Cavanagh, M., Dacey, L., Findell, C., Greenes, C., Sheffield, L., & Small, M. (2001). Navigating through number and operations in prekindergarten-grade 2. Reston, VA: National Council of Teachers of Mathematics.

Confer, C. (2005). Teaching number sense: Kindergarten. Sausalito, CA: Math Solutions.

Richardson, K. (1999). Developing number concepts counting, comparing, and pattern. White Plains, New York: Dale Seymour Publications.

Van de Walle, J., Karp, K., Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally. (7th ed.) Boston, MA: Allyn & Bacon.

Van de Walle, J. & Lovin, L. (2006). Teaching student-centered mathematics grades k-3. Boston, MA: Pearson Education.