Count by Groups

Overview

This is Lesson 22 of 30 in Building Mathematical Thinking. Students practice counting by 2s, 5s, and 10s, then connect skip-counting sequences to equal groups arranged in rows. Movement, rhythm, visual patterns, and concrete objects support learners across kindergarten through fifth grade.

Learning intentions

Students will be able to:

• Say and continue counting sequences by 2s, 5s, and 10s.
• Model skip-counting with equal groups of objects.
• Write an addition equation using equal addends to represent an array.
• Explain how the number of groups and objects in each group connect to the counting pattern.

Success criteria

• I can count by 2s, 5s, and 10s.
• I can complete a skip-counting sequence.
• I can make equal groups and count the total.
• I can write an addition equation to match my groups.

Curriculum links

• Number and Operations in Base Ten — read, write, and count whole numbers using place-value patterns.
• Operations and Algebraic Thinking — use addition to find the total in rectangular arrays and write equal-addend equations.
• Mathematical practice — use models, patterns, reasoning, and explanations to solve problems.

Lesson structure (30 minutes)

1. 0–4 min · Hook and movement count. Teacher opens the opening question and movement-count slides and asks, “How could we count 20 objects quickly without counting every object?” Students stand beside their desks and clap, tap, or step while counting by 2s, then repeat by 5s and 10s.

2. 4–9 min · Make the pattern visible. Teacher displays a large number chart from the highlighted number-chart slides and highlights the numbers reached when counting by 2s, 5s, and 10s; teacher briefly points out that the pattern repeats in the ones and tens places. Students echo-read each sequence and identify what changes and what stays the same.

3. 9–15 min · Connect groups to counting. Teacher uses counters or linking cubes to build arrays such as 3 rows of 2, 4 rows of 5, and 2 rows of 10, narrating: “Each row has the same number, so I can count equal groups.” Students build one array at a time with a partner, touch each group, and count aloud by the group size. Teacher asks, “How many groups? How many in each group? What is the total?”

4. 15–22 min · Guided worksheet practice. Teacher distributes the skip-counting and equal-groups worksheet and models the first item, completing a sequence before drawing or matching the equal groups. Students complete one sequence at a time: first by 2s, then by 5s, and then by 10s. For each item, students draw groups or an array and write an addition equation such as 5 + 5 + 5 = 15. Students may say answers to an adult or partner instead of writing every response.

5. 22–27 min · Partner challenge and discussion. Teacher returns to the partner-problem and discussion slides and shows an array or grouping problem, such as “There are 4 groups of 5 counters. How many counters are there?” Students build or sketch the groups, count by 5s, and tell a partner the matching equation. Partners use the sentence frame, “I counted by ___ because each group has ___.”

6. 27–30 min · Exit check and closure. Teacher displays the closing and exit-check slide and gives each student one prompt: “Complete 10, 20, __, __ and show it as equal groups,” or “Complete 5, 10, __, __ and write an addition equation.” Students respond orally, with counters, by pointing, or on a small response board. Teacher asks one or two students to explain how their groups matched their counting sequence.

Resources

• the complete counting-by-groups slide deck
• the skip-counting and equal-groups worksheet
• Large 1–100 number chart
• Counters, linking cubes, or small classroom objects
• Mini whiteboards and markers
• Highlighters or colored pencils
• Optional rhythm instruments or a steady beat

Assessment

• Listen during movement and partner counting for accurate sequences and one-to-one correspondence.
• Check whether students make equal groups, identify the group size, and connect the groups to an equal-addend equation.
• Use the final prompt to record whether each student can continue a sequence and represent it with groups, objects, or an equation.

Differentiation

• For students needing support, teach one sequence at a time, use a 1–100 chart with the target numbers highlighted, provide counters and partially completed sequences, and count together with a steady rhythm.
• Offer movement, songs, clapping, tapping, and oral rehearsal before writing. Allow students to point, build, speak, or dictate responses.
• Provide dyslexia-friendly access through large, uncluttered charts, clear sans-serif print, strong color contrast, highlighted sequences, short directions, and minimal copying. Read worksheet directions aloud.
• For students ready for more challenge, ask them to create an array and write its equal-addend equation for a partner to solve, or explain how the same total can be counted by different group sizes.

Extension

• Students solve a money problem using skip-counting, such as finding the value of four nickels or three groups of two dollars.
• Students solve a grouping problem: “There are 30 objects. Show two different ways to make equal groups and write an addition equation for each.”