Extend your students’ place value understanding with this set of task cards, resource materials, and assessment activities. With this “print-and-go” resource, you’ll have everything you need to enrich, strengthen, and assess your students’ understanding of place value relationships.
Common Core State Standards for Mathematics addressed:
Number and Operations in Base Ten (NBT)
Generalize place value understanding for multi-digit whole numbers.
• Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. (4.NBT.1)
This set is a follow-up to Set A of my From Place to Place
task cards & printables, available here
. The materials in Set B are unique and different from the materials in Set A. This set has no duplicate materials from Set A.
• graphic reference sheet
• interactive foldable flap book
• 32 task cards
• task card answer sheet and key
• 8 self-checking “answer cards”
• 2 assessment activities and scoring guide
About the Cards
This set of resources is designed to build a full understanding of place value relationships in whole numbers through ten millions. The resources involve comparisons between both consecutive places
– such as hundreds to tens or millions to hundred thousands – and non-consecutive places
– hundred thousands to hundreds or thousands to tens, for instance. Some of the comparisons on the cards in this set involve determining what digit is 10 times larger than a given digit (e.g., “Which number has a 3 that is worth 10 times as much as the 3 in the number ______?”), but most ask students to consider which digit is 100 times the size (shifted two places to the left) or 1,000 times the size (shifted three places to the left). The cards in this set are more challenging than the cards in Set A, but they provide an excellent extension to that beginner set, building on the idea that shifting a digit one place to the left increases its value by 10 times and pushing the students to see broader patterns in the place value system. If you are looking for introductory place value materials, check out Set A here
There are four different question types that alternate on the cards. The variety of question types will push your students to think deeply about place value relationships, while the repetition of the question types will allow them to practice and build proficiency with the place value comparisons each question type requires. As the students respond to the cards, they will have to make comparisons between digits in different numbers, create their own numbers to match given criteria, and relate two different types of numeric expressions (such as “500 x 100” or “600 tens”) to the value of digits in a multi-digit number.
I organized the cards in this set progressively, building from question type to question type. I chose the order based on my experience with my own students and the questions that they consistently have had more or less difficulty with. Cards 1 through 8 are the easiest, relatively, asking students to simply compare a given digit in one number to a given digit in another number, looking for a digit that is 10x, 100x, or 1,000x larger than another specified digit. Cards 9 through 16 ask the students to use specific digits to create a number of their own that have a particular digit that is 10x, 100x, or 1,000x larger than the same digit in another, named number. Cards 17-24 are more challenging than the first sixteen, asking the students to identify an arithmetic expression (such as 50 x 100 or 700 x 1,000) that is equal to the value of a given digit in a named multi-digit number. The final eight, cards 25 through 32, are the most challenging – similar to cards 17-24 –, asking students to consider the value of a digit in terms of a different place (e.g., is 70,000 equal to 700 tens or 700 hundreds?).
Please check out the preview to see all of the materials in Set B up close!
Using the Cards
Since the cards are organized into 4 groups of 8 similar cards, your students can have repeated practice with a particular problem type, allowing them time to learn from their errors and master one particular aspect of the target standard before moving on to another problem type. In addition, because each group of cards builds in difficulty from the previous group, the set offers various opportunities for differentiation. Students who are still building an understanding of place value relationships can work on cards 1-8 while your students who are a little further along the place value continuum can start with cards 9-16 or 17-24. Alternately, your students who need the most practice can work through all the cards in order, getting the maximum amount of practice, while your students who have a firmer grasp of place value relationships can do just the odd or even cards, working on all the problem types but completing fewer cards. You might use the first two cards in each group of 8 as guided practice, have students work in pairs on the next three or four cards, and then complete the final two or three cards on their own, repeating this procedure with each group of 8 cards.
There are lots of ways in which you can implement the task cards beyond the suggestions above. You can have the students work on them independently, working through the task cards on their own. The students can work on them in pairs or small groups, completing a given number of cards in one or more sessions. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. You can even use them as a variation of “problem of the day”, giving each student 1 sheet of 4 cards to glue in their journals and solve, one sheet per day for eight days.
Reinforcing the Concept
You may choose to introduce or follow-up the cards with the included reference sheet and interactive foldable flap-book. The reference sheet, designed to be glued in your students’ math notebooks, provides an overview of place value relationships using whole numbers through millions. A labeled place value chart presents pairs of numbers and describes the relationship between consecutive places. Another chart and set of labels walks your students through a comparison of digits that are two places, rather than just one place, apart. Your students can use the journal insert as a guide while they work on the cards, as well as when they complete other tasks that relate to place value. In addition, you can use the reference sheet as the springboard to a class discussion about place value relationships; below the examples, there is an open-ended question about the effects of moving a digit three places to the left. You can have your students discuss and respond to the questions in their journals.
The interactive foldable offers a chance for your student to practice representing a digit’s value in a variety of ways, similar to the representations used on the cards. Work with your students, or have them work in groups or pairs, to represent numbers using verbal and numeric expressions (e.g., 20,000 = 200 hundreds and 20,000 = 200 x 100). A series of flaps allows students to represent specific numbers in terms of tens, hundreds, and thousands, as the cards do. Working through this foldable will help your students build their understanding of the relationship between the places, as well as providing a handy tool to refer to when working on the cards or other place value activities.
Assessing Student Understanding
The two assessment activities can be used to evaluate student understanding of place value relationships. The pairs of activities are formatted similarly, and have similar types of questions, though the numbers on each are different. You can use these activity pages in a variety of ways. You could give one as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give the second worksheet as an independent post-test. You could also have the students work on the task cards, then complete one of the worksheet as guided practice with yourself, a partner, or a small group, and then give the second worksheet as an independent assessment. The worksheets could also be given as homework, center assignments, or any other purpose that fits your teaching style or classroom routines.
For more resources to build your students’ understanding of number relationships, please check out the other related resources I have available –
Rounding the World - rounding whole numbers task cards & printables (set a)
Self-Checking Math Riddles – Rounding to the Nearest 10 and 100
Snow Bonds: x and ÷ with multiples of 10 task cards & printables (set b)
It's All Relative – multiplication and division number relationships game
Placing the Value - task cards + printables set
I hope your students enjoy these resources and are able to build their proficiency with place value. – Dennis McDonald