Number sense activities: teaching with manipulatives

Number sense is a student's feel for what numbers mean: how big 8 is, that 8 is 2 less than 10, that 47 is closer to 50 than to 40. Students with weak number sense often count everything from 1, guess wildly on estimates and treat every new fact as something to memorize. Manipulatives give them a way to see and touch the relationships.

This page orders the activities from earliest to latest, explains each one, and follows one fictional student through a semester. For goal wording, see the number sense goals and early numeracy goals pages. For the wider math area, see the math IEP goals pillar.

What to check before you start

Run a 10-minute check with counters and cards to find the starting activity:

• Counting a set: can the student count 10 scattered objects, touching each once, and say how many?
• Subitizing: shown 1 to 5 dots for 2 seconds, can the student name the amount without counting?
• Numerals: can the student read numerals to 20 and match them to sets?
• Partners of 10: shown 7 on a ten-frame, can the student say how many more make 10?
• Number line: can the student mark about where 50 goes on a line from 0 to 100?

Start at the first item the student misses. The federal practice guide on teaching math to young children recommends teaching number in a developmental progression, so each activity builds on the last.^[1] The order below follows that idea.

Step-by-step: number sense activities in order

Step 1: Counting objects one by one

Line up 5 to 10 counters. The student slides each one across a line on the table while saying one number. Moving the counter is what builds one-to-one correspondence: one object, one word. Then ask "How many?" and wait for the last number, not a recount. Scatter the counters once lines are easy.

Activity: "Feed the frog." The student counts the number of pompoms the card shows into a cup with a frog face, one at a time.

Step 2: Subitizing small amounts

Flash a dot card or a ten-frame for about 2 seconds and ask how many. Start with 1 to 3 dots, then 4 and 5 in dice patterns, then scattered. Subitizing lets students stop counting small amounts and is the start of seeing numbers as parts.

Activity: "Peek under the cup." Hide 1 to 5 bears under a cup, lift it for 2 seconds, and ask how many.

Step 3: Building numbers on ten-frames

Give a blank ten-frame and counters. The student builds a number, fills the top row first, and says it two ways: "7 is 5 and 2" and "7 is 3 away from 10." Ten-frames make 5 and 10 into anchors, which later drive the making-ten strategy for facts.

Activity: "Make 10." Show a ten-frame with 6. The student adds counters to fill it and writes 6 plus 4 equals 10.

Step 4: Number lines and comparing

Use a floor number line from 0 to 20 the student can walk on. Ask the student to stand on 8, then jump 3 more. Then move to a paper line marked only at 0 and 20, and later 0 and 100, and ask the student to mark where a number goes. Federal guidance on elementary math intervention recommends number lines as a core representation for whole numbers, fractions and operations.^[2]

Activity: "Closer to." Place 0, 10 and 20 on a line. Draw a card (14). Is it closer to 10 or 20? Mark it, then check by counting.

Step 5: Bundling tens

Give 20 to 60 loose straws and rubber bands. The student bundles groups of 10 and counts the bundles by tens, then the loose straws by ones. Then switch to base-ten blocks. This is the bridge to place value.

Activity: "Straw shop." The student is asked for 34 straws and must hand over 3 bundles and 4 loose straws, not 34 loose ones.

Step 6: Connect objects to numerals every time

After each activity, write the numeral or equation next to the objects. A student who builds 6 and 4 on a ten-frame but never sees "6 + 4 = 10" may not link the two. Say it, build it, write it.

Step 7: Keep it short, daily and in routines

Five to 10 minutes a day beats one long lesson a week. Fold number sense into routines: count the students at the door, check how many snacks are left, compare the number of sunny and rainy days on a chart. The young children practice guide recommends teaching math every day and weaving it into the school day.^[1]

Worked example: one student from start to finish

Ava (fictional) is in kindergarten. In September she counts aloud to 20 but recounts from 1 when asked "how many?" and touches some objects twice.

Baseline (3 sessions). Counting a set of 10 scattered objects correctly: 1, 2 and 1 of 5 trials. Median: 1 of 5. Subitizing 1 to 5 dots: 3 of 10 cards. Partners of 10: not attempted.

Goal. Given 5 to 15 objects, Ava will count by moving each object once and say the total without recounting on 4 of 5 trials, across 3 sessions. (Template: move each counter aside as it is counted.)

Weeks 1 to 3: counting by moving. Feed the frog, 10 trials a day with sets of 5 to 8. Correct counts rise from 1 of 5 to 4 of 5 with sets under 8.

Weeks 4 to 6: larger and scattered sets, plus subitizing. Sets of 8 to 15. Counting holds at 3 to 4 of 5. Subitizing 1 to 5 dots climbs from 3 of 10 to 8 of 10.

Weeks 7 to 10: ten-frames. Ava builds numbers to 10 and starts saying "5 and 3 is 8." Counting reaches 4 of 5 trials across 3 sessions in week 9. Goal met. The team adds a goal for answering how many with the last number counted with sets of 11 to 20.

Each probe was graphed weekly. Short repeated probes are how a team decides whether to keep the plan or change it.^[3]

Common mistakes and better choices

• Weak: Counting pictures on a worksheet from day one. Better: Real objects the student can move, then pictures.
• Weak: Accepting a recount when you ask "how many?" Better: Teach that the last number said tells how many.
• Weak: Using manipulatives for weeks without writing numerals. Better: Build it, say it, write it in every session.
• Weak: Number lines with every number labeled forever. Better: Fade labels to 0 and the end so the student has to estimate.
• Weak: Base-ten blocks before the student can count a set of 20. Better: Bundling straws after counting and ten-frames are solid.
• Weak: Too many manipulatives on the table at once. Better: One tool per activity, put away before the next.

Tools and templates

• Counters, ten-frames, dot cards, a floor number line, straws with rubber bands, base-ten blocks.
• Early numeracy goals for counting, subitizing and cardinality templates.
• Number sense goals for comparing, number lines and place value.
• Opportunity data sheet for trial-by-trial data on counting and ten-frame tasks.
• Teaching money skills, which builds on counting by 5s and 10s.
• The goal checker to test a goal draft.

Frequently asked questions

Use it in IEP Atlas

• Number sense goals (math)
• Early numeracy goals (math)
• Number sense in the IEP glossary
• One to one correspondence in the IEP glossary
• IEP goal checker

Related guides

• IEP goals for math: calculation, problem solving and functional math
• IEP goals for place value
• Teaching money skills (next-dollar, coin counting)
• Concrete-representational-abstract (CRA) for math goals
• Teaching time and elapsed time in special education

Sources

1. Teaching Math to Young Children, What Works Clearinghouse, Institute of Education Sciences
2. Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, What Works Clearinghouse, Institute of Education Sciences
3. Progress Monitoring: Data & Goal Setting, National Center on Intensive Intervention

Written and checked by the IEP Atlas editorial team under our editorial policy. This guide describes general practice and federal rules. It is not legal advice; your state may add requirements, and the IEP team makes the decisions for each student.