Place Value to 100

Strand: Number
Outcomes: 5, 6, 7

Step 5: Follow-up on Assessment

Guiding Questions

What conclusions can be made from assessment information?
How effective have instructional approaches been?
What are the next steps in instruction?

A. Addressing Gaps in Learning

If a student continues to have problems with place value, return to making various numbers to 99 with manipulatives and connecting them with the numerals they represent both with number flips and pictorially.

Begin with numbers closer to 20 than 100 and gradually increase the quantities.
Continue the activity and ask probing questions so that students can develop some meaning for the numbers and an understanding of the relationship between the numbers and their corresponding numerals.
Begin with the easier questions such as, "What numbers are one more/less?" and move on to questions such as, "How much would we have if we added ten?" Check that the student’s difficulty with an activity is not a result of some other learning challenge and not actually conceptual.
If the student has difficulty with scribing, be sure to provide opportunities for the student to assess the number of items from a picture or diagram and show the numeral with sets of cards.
The student can also ascertain the quantity on various place-value mats, rather than from diagrams. Van de Walle and Lovin (2006) point out that although physical models for base-ten concepts play a key role in helping students understand the idea of "a ten," students must construct the concept and impose it on the model; the model does not show the students the concept (p. 127).

If students have language or organizational problems that make it difficult for them to explain their actions and thoughts, provide question prompts that lead them from step to step, such as:

What does the 3 in 37 mean?
Which manipulatives should you use to represent the 3?
How many do you need?
Where will you place them on the place-value mat?
What does the 7 stand for?
Which manipulatives should you use for the 7?
How many do you need?
Where will you place them?
Show the numeral with the number flips.
How is it read? Repetition and gradually reducing prompts will help students be able to use the language of math to express themselves.
If students are reversing digits in written numbers, for example printing 42 for 24, draw attention to the difference in value based upon the numeral’s place.
Ask them if their allowance were 75¢, would they be satisfied if their parents gave them 57¢ instead?
If the student has not just made a careless error and really does not understand place value, he or she will need to be shown the difference between these quantities with pennies and perhaps even some examples of how much more could be bought with the greater value.
In this case, return to more manipulative work with smaller quantities.

B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Consider strategies such as the following:

Challenge students to make up as many combinations of tens and ones for a number as possible. Students might keep their own notebooks, beginning with 21 and add to this until they reach 99 or 100. For example, under 21 they would record 2 tens 1 one and 1 ten and 11 ones; under 32 they would record 3 tens + 2 ones, 2 tens + 12 ones and 1 ten and 22 ones. It may be helpful to the whole class if students contribute these examples to a large classroom chart.
Encourage parents to give students opportunities to count quantities that range from 25 to 100, and provide means of organizing the items into tens and ones. For example, pennies, empty pop cans, pieces of pasta like macaroni, cereal, cards (Christmas or business), buttons, paper clips and small candies. Small bowls, margarine or yogurt containers, envelopes and plastic bags are all suitable for organizing groups of ten. Paper clips can be slipped together to make strings of ten.
Encourage the students and their families to take part in preparing containers for estimation. If the family has a container that is transparent they can do without, have them fill it with small things to be counted and send it to school. Students and their families should do a count of the items they send beforehand and submit their counts. After the children have predicted the quantity in the container and the count has been verified by the students, the container should be refilled with at least one other set of items to be counted.
Encourage parents to ask their children to estimate as they go through their household activities each week. For example, students could estimate how many litres of gasoline the car will take, how much the grocery or restaurant bill will be, how long it will take to play a game, and how tall each member of the family is in centimetres. With repeated opportunities for making estimates, the students should be able to give more and more accurate estimates. The second time students estimate how many litres of gasoline the family vehicle will take, they may confirm that it is as empty as last time and then make an estimate.