Build Numbers to Twenty

Overview

In Lesson 14 of 30 in Building Mathematical Thinking, students compose numbers from 11–20 using objects, ten-frames, and numerals. The lesson builds from counting and recognizing quantities toward understanding that numbers 11–20 are one group of ten and some additional ones.

Learning intentions

Students will be able to:

• Build a number from 11–20 with objects on a double ten-frame.
• Represent the same number with a drawing and a numeral.
• Explain that numbers from 11–19 are made of ten ones and additional ones.
• Use addition language to describe a number, such as “18 is 10 and 8 more.”

Success criteria

• I can make a number with objects on ten-frames.
• I can show the number with a drawing and a numeral.
• I can say how many tens and ones are in my number.
• I can show the same number in more than one way.

Curriculum links

• Number and Operations in Base Ten: composing and decomposing numbers from 11–19 as ten ones and additional ones.
• Number and Operations in Base Ten: understanding that digits in a two-digit number represent tens and ones.
• Operations and Algebraic Thinking: representing addition with objects, drawings, verbal explanations, and equations.
• Counting and representing numbers within 120, with appropriate extension for older or ready students.

Lesson structure (30 minutes)

1. 0–4 min · Hook and activate prior knowledge. Teacher opens the hook and number-building introduction and displays a full ten-frame with 4 additional counters, asking, “How many are there? How do you know?” Students count, turn and tell a partner, and share a representation of 14.

2. 4–9 min · Model composing a number. Teacher uses large, color-coded ten-frames and counters to model 17, explicitly grouping ten counters and saying, “17 is one ten and seven ones.” Teacher records 17 and 10 + 7 on the tens-and-ones modeling slides. Students build 17, touch-count the ten, count the extra ones, and repeat the sentence using oral vocabulary.

3. 9–13 min · Guided practice. Teacher reveals 12, 15, and 19 one at a time on the guided practice slides. After each number, the teacher asks, “How many tens? How many ones? What equation matches?” Students build each number with counters, show it to the group, and explain their thinking. Check that students do not treat the two digits as unrelated numbers.

4. 13–23 min · Partner number build. Teacher pairs the 10 students and distributes the number composition practice sheet and double ten-frames with counters. Each partner chooses or receives a number from an individualized range, builds it, draws the ten-frame representation, writes the numeral, and completes an equation such as 16 = 10 + 6. Partners switch roles as builder and checker for at least two numbers. Teacher circulates and asks, “Where is your group of ten?” and “How does your drawing prove the numeral?”

5. 23–27 min · Compare representations. Teacher asks selected students to display two different representations from the number composition practice sheet and prompts, “What is the same? What is different? Which representation makes the ten easiest to see?” Students compare using the sentence frame, “Both show __ because __.” Ready students show one number with objects, a drawing, an equation, and place-value words.

6. 27–30 min · Exit check and share. Teacher displays a final number on the exit and reflection slide and asks students to independently build or draw 18, write its numeral, and complete “18 is ___ ten and ___ ones.” Students briefly share with a partner while the teacher collects responses and notes who can compose and explain the number.

Resources

• the complete number-composition slide deck
• the number composition practice sheet
• Large double ten-frames
• Individual double ten-frames
• Two colors of counters or linking cubes
• Pencils, crayons, and dry-erase boards
• Optional tactile counters or magnetic numbers
• Teacher observation checklist

Assessment

• During modeling and guided practice, listen for accurate counting, grouping of ten, and use of “ten” and “ones.” Ask students to prove their answers with objects.
• During partner work, check whether each student can match a built quantity, drawing, numeral, and equation. Record whether support was needed.
• Use the exit response for the number 18 to identify students ready to work within 11–19, students needing a smaller range, and students ready to extend beyond 20.

Differentiation

• Support: Begin with 11–15, provide a prefilled numeral, use a partially completed ten-frame, and offer the sentence frame “__ is one ten and __ ones.” Count aloud together and allow students to build before writing.
• Dyslexia-friendly access: Use large, uncluttered ten-frames, color-code the group of ten and extra ones, provide oral directions and vocabulary, minimize copying, and offer tactile counters, linking cubes, or magnetic numerals. Read all worksheet directions aloud.
• Individualized ranges: Students who need intensive support work with 11–13 or 11–15; students working at grade level use 11–19; students ready for more challenge work with 20 and numbers within 120 using tens and ones.
• Advanced learners: Show a number in several ways—objects, double ten-frame, drawing, equation, and words—and compare which representation communicates the tens and ones most clearly. They may explain why 20 is two tens and zero ones.

Extension

• Ask advanced students to choose a number from 11–20, represent it in at least four ways, and write a comparison with another number: “__ is greater than __ because it has __ more ones.”
• Invite students to change one number by adding or removing one counter and explain how the numeral and equation change.