Fill a ten-frame and build fluent facts within five

Learning goal: Find a partner that makes ten for starting amounts one through nine, and develop accurate, increasingly fluent addition and subtraction within five. These are related activities but different targets. A ten-frame supports making ten; repeated small-number reasoning supports fluency within five. Plan brief practice on several days rather than a single timed test.

A ten-frame is a rectangle with two rows of five equal spaces. Each space can hold one counter. The frame’s capacity is ten counters; the number currently present may be less than ten. In the illustration, seven spaces contain counters and three are empty. Read the quantity label as “seven counters present; three spaces to fill,” not “ten counters present.”

Put seven counters into the frame, filling the top row before continuing into the bottom row. Count the empty spaces and place a new counter in each: one, two, three. The filled frame now contains ten. Therefore seven needs three more to make ten, or 7 + 3 = 10. Three counts the added counters; ten counts all counters after the action.

Try starting with four. Four spaces are occupied and six are empty, so six more counters fill the frame. Ask what happens to the needed partner as the starting amount grows. If one additional space is already filled, one fewer remains empty. Use every starting number from one through nine across repeated sessions, with drawings or equations recording the results.

For fluency within five, build small facts from relationships. Three and one make four because one more than three is four. Four take away one leaves three. Two and two make four; four can be separated into two and two. Fluency means the learner responds accurately and efficiently using understood relationships. It does not mean that a child must perform under a stressful stopwatch. A learner may initially use fingers or counters, then need them less often.

Keep the range explicit. A ten-partner task may use 8 + 2; the fluent-fact practice in this lesson stays within five. Success with one memorized partner pair is not evidence that every make-ten or within-five fact has been learned.

Worked example 1: Nine needs one. Fill nine spaces of a ten-frame. Only one space remains empty. Add one counter, recount ten and record 9 + 1 = 10. If a learner says ten more are needed, distinguish the frame’s total capacity from its unfilled portion.

Worked example 2: Use a known small fact. Show two counters and add one. The total is three, so 2 + 1 = 3. Remove the added counter to show 3 − 1 = 2. Explain both actions, then practice without the objects while allowing them for checking.

Worked example 3: Read zero correctly. Five counters are present and none are removed. Five remain: 5 − 0 = 5. Zero describes no removal, not an instruction to erase the original set. Similarly, adding no counters to three leaves three.

Guided practice: In changing order, show frames containing 2, 5, 8, 1 and 6 counters. Ask how many more would make ten and verify by filling the spaces. Later include the other starting quantities. For fluency, use a small mixed set such as 1 + 2, 4 − 1, 2 + 2, 5 − 2 and 3 + 0. Invite an explanation for one fact each session.

Independent assessment across days: Demonstrate a make-ten partner for every starting quantity 1–9, using a drawing or objects when needed. Separately sample addition and subtraction results within five in mixed order on at least three occasions. Record accuracy, strategy and amount of prompting; do not assign an unsupported state proficiency score.

Feedback: Recounting every space is a valid beginning strategy. Help the learner notice five-filled rows, then combinations within the second row. For incorrect small facts, return to the action and relate it to a known fact. Extend by asking the child to create a correct fact and its related taking-away story.