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TouchMath Extend

Lesson 7: Numbers 13–15

Lesson Objectives

  • Represent place value with concrete and pictorial models  
  • Relate place value to the concept of number 13, 14, and 15.  
  • Use place value models for numbers 13-15  
  • Read and write the numbers 13-15 
  • Compare numbers using place value charts and number lines  


  • Extend Workbook (Page 7) 
  • Counters or objects for counting 
  • Number Line to include 11-20 
  • Linking cube manipulatives or other stacking manipulatives (to total 13-15) 
  • Beads and strings 
  • Place value mats 
  • Whiteboard with dry erase markers and erasers 
  • Straws and rubber bands (optional) 
  • Ten frames (optional) 
  • TouchMath’s TouchPoints with Pictures (TPP) and without pictures (optional) 

Step 1: Warm Up (5 min)

Remind students that they have represented 10, 11, and 12 in many ways and that they all show the place value of the number. They will now work with numbers 13-15. They will first build bundles of 10, using maniupulatives of your choosing (beads on a string, linking cubes, straws and rubber bands, or ten frames). Have them review by adding an extra manipulative next to their bundle of 10 to represent 11 and 12. 

Step 2: Vocab Review (5 min)

Review the word “bundle” used in the warm-up and explain a bundle means a group. Show 1 bundle of 10 beads and explain this is “one group of 10” and there is not any left over, so no “ones.” Any “extra” after you have bundled a group of 10 would represent “ones.” Show them the place value chart and tell them you will be practicing with “tens” and “ones” today. Show them linking cubes. 

Step 3: Model (5 min)

Take your linking cubes, beads and strings, or straws and rubber bands and work through grouping groups of 10 and an extra three/four/five objects to represent 13-15, as well (e.g. a bundle of 10 beads on a string with 3 extra next to the bundle, would represent 13). Play around with various ways, making groups of 10, and having 3-5 extra. Draw a group of 10 (e.g. stars) on a white board and circle the group of 10. Then draw one star outside of the circle to represent 11, and then another star to represent 12. 

Step 4: Guided Practice (5 min)

Tell students that they have represented 10, 11, and 12 in many ways, and they all show the place value of the number. It is 10 objects, or 1 bundle of 10 and zero ones on the place value chart. It is a two-digit number: tens and ones. Give students different manipulatives to play around with and work with students to make a bundle of 10, then a bundle of 10 with 3/4/5 extra (13/14/15). Students may also use white boards and draw a group of 10, circling the group and making 3/4/5 extra outside of the circle to represent 13/14/15. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (7). Direct students to the number line at the top of the page. Have students point to each number on the number line and say each number aloud: 11, 12, 1320. Review place value with students. Have students link 10 linking cubes together to represent one group of 10, with three ones. Then, have students trace over “1” under the tens to represent one group of 10, and 3 to represent three ones. After that, have them write 13 on the line to the right. Repeat for number 14 and 15, placing an extra 3 or 4 cubes next to the group of 10 they have already made to represent “14 and 15.” Have students trace 14 and 15 in the place value box and explain the meaning of place value with 14 and 15. 

Step 6: Wrap Up (5 min)

Review lesson objectives, key vocabulary words, place value, and linking cubes.