Understanding tens and units in first-grade math
The basic premise of place value instruction at this level is straightforward: show students that ten individual objects can be grouped together and treated as a single unit called a ten. This concept underpins every arithmetic operation they will encounter from second grade onward. The difference between success and failure in this topic usually comes down to how long students spend with concrete materials before being asked to work with abstract notation. I have watched this topic go poorly when teachers rush the transition from objects to paper. A student who can correctly count out 35 blocks will draw the number 53 without hesitation if the connection between the visual grouping and the written digits was never solidified. The error is systematic, not careless. It means the student does not understand the place value system; they are simply copying shapes they see on the board.
Common pitfalls in teaching atividade de matematica 1 ano dezenas e unidades
One mistake I encounter constantly is presenting the concept through worksheets too early. Children need to physically handle groups of ten before they can make sense of the written column format. A child who has never held a bundle of ten straws or ten counter chips alongside loose single counters will treat the tens column and the ones column as two unrelated labels. They might write 71 for the number 17, or worse, they will add the digits and produce 8 for 53. This is not a calculation error. It is a conceptual gap. Another frequent issue involves the way textbooks introduce the terminology. The Portuguese words dezena and unidade are used inconsistently across different publishers. Some books call the tens column "casa das dezenas," others use "ordem das dezenas," and some avoid the word casa entirely because of confusion with geometric shapes. This inconsistency forces teachers to spend extra class time clarifying vocabulary rather than building number sense. I have stopped asking students to fill in diagrams labeled "D" and "U" unless I also explicitly teach what those abbreviations mean in context. Without that bridge, the letters are just another symbol to memorize.
The transition from concrete to semi-concrete to abstract typically takes between three and six weeks depending on the class. Some students move through it in two weeks. Others need eight. The material should stay concrete until the student can reliably draw a correct representation, not until the teacher finishes the scheduled lesson plan. I track this by having students solve three problems using base-ten blocks and then immediately solve three similar problems using only drawings. If the accuracy rate drops below 70 percent between the two formats, they need more concrete practice before moving on.
Practical approach for structured practice
The most reliable progression follows this sequence: physical manipulation of materials, drawing grouped representations, solving problems on grid paper with columns, and finally working on standard worksheets. The grid paper stage is the one most often skipped. Students who jump straight from blocks to blank worksheets frequently produce answers that look correct but rest on fragile understanding. Grid paper forces a spatial separation between the tens and the ones that matches the mental model the student is still building. When designing or selecting exercises, look for activities that require both decomposition and composition. A student who can only break apart a number like 46 into 40 and 6 has partial understanding. They also need to construct 46 from 4 bundles and 6 loose items. The skill is bidirectional. Many commercial worksheets only ask for one direction, which creates a blind spot that shows up later when students struggle with addition with carrying.
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There is a specific problem type that reveals whether a student truly grasps place value or is just following a procedure. Ask the student to represent the number 60 using base-ten blocks. Some will lay out six single bundles and leave no loose units. Others will incorrectly include a single unit. The error is subtle but telling. It suggests the student treats zero as invisible rather than as a positional placeholder that maintains the structure of the number. This concept does not usually surface again until third grade, but the foundation should be laid here. For free printable exercises, the standard resources available from major educational publishers cover decomposition, comparison, and ordering of two-digit numbers. These are sufficient for classroom reinforcement. One resource that tends to work well is the collection from Brasil Escola, which includes exercises on decomposing numbers into tens and ones, identifying the value of each digit, and ordering two-digit numbers. The material is formatted for direct printing and requires no special software.
Building practice into daily routine
A ten-minute daily exercise focused on this topic is more effective than a single thirty-minute session once a week. Spaced practice reinforces the connection between the concrete and the abstract without requiring extensive preparation. The exercises should alternate between representation tasks, where students draw or build numbers, and computation tasks that use the place value structure, such as simple addition within 100 without carrying. Students who struggle with this topic often have a secondary issue with number sense outside of place value. If a student cannot reliably compare two numbers below 20, they will not succeed with tens and units. The comparison skill should be assessed before the place value unit begins. A quick oral check where the teacher says two numbers and the student identifies the larger one takes less than two minutes and prevents a lot of downstream frustration.
There is a limitation worth stating plainly: this topic cannot be mastered through passive completion of worksheets. No amount of filling in blanks will substitute for the student actively constructing the relationship between quantity and notation. Activities that require the student to move, draw, or explain their reasoning out loud produce measurably better retention than silent worksheet completion. The trade-off is that these activities require more teacher preparation and classroom management effort. That effort is not optional if the goal is genuine understanding rather than temporary compliance. The progression from concrete materials to abstract notation is the central challenge in this topic. Treat the concrete stage as essential, not as an introductory warm-up that can be compressed. When students reach the worksheet stage with a solid foundation, the exercises become reinforcement rather than introduction. The difference in student performance between those two starting points is significant.
One detail that matters more than textbooks usually acknowledge is the role of oral language. When a student says "trinta e cinco" while pointing to three bundles and five singles, the verbal label and the physical representation are linked. When the student writes 35 without that link, the notation is hollow. Having students say the number aloud while they represent it, even after they have moved past the manipulative stage, keeps the connection active. It is a small habit that prevents the drift into procedural empty work. The ultimate measure of whether the exercise is working is not whether the student can complete the sheet, but whether the student can explain why the digit in the tens place represents a different quantity than the digit in the ones place. A correct answer without that explanation indicates the student has learned a rule, not a concept. Rules are forgotten. Concepts are rebuilt. The difference matters well beyond first grade.
