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33.43 MB | 36 pages

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33.43 MB | 36 pages

Build your students’ understanding of multiplying with decimals with this “print-and-go” resource – 64 task cards , 2 reference sheets, and 8 assessment activities. It’s everything you need to develop, strengthen, and evaluate your students’ ability to fluently multiply simple decimals.

____________________________________________________________________

Common Core State Standards for Mathematics addressed:

**Numbers and Operations – Fractions (NF)**

*Perform operations with multi-digit whole numbers and with decimals to hundredths.*

• Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (5.NBT.7)

____________________________________________________________________

Included:

• 2 reference sheets

• 2 sets of 32 task cards

• task card answer sheet and key

• 8 self-checking “answer cards”

• 8 assessment activities

• rubric and answer key for assessment activities

This set of task cards is designed as a follow-up to Set A of my*Brainy Birds* task card and printables set. That set focuses on multiplying and dividing whole numbers and decimals by powers of ten (e.g., 4.5 ÷ 100 and 68.92 x 10^3). If you are looking for a beginning resource for multiplying and dividing decimals, that set may be a useful starting point.

**About the Cards**

This set of cards focuses on multiplying decimals by decimals and decimals by whole numbers. The highest place in the factors is the hundreds place, and none of the factors or products have digits any lower than the hundredths place. All of the factors have only one non-zero digit (for instance, 400, 7, 0.02, and 0.9), which allows students to be able to use basic facts to mentally multiply the factors.

*Please check out the preview to see the cards and other materials up close!*

There are two sets of 32 task cards, and the questions and answers on the two sets do not overlap. Each card in Set B1 presents students with a multiplication expression and simply requires students to find the product, while Set B2 has students apply their understanding of decimal multiplication to perform a variety of tasks, such as comparing expressions and identifying the value of a variable. Each set uses a different color border (blue for Set B1 and purple for Set B2). In addition, each card is labeled as belong to Set B1 or Set B2 to help distinguish them if you decide to print the cards in grayscale. [The simple graphics on each card look great in b & w or color!]

**Using the Cards**

When I taught multiplication with decimals, I began with simple expressions like the ones on these cards: 0.3 x 8, 0.04 x 7, 0.9 x 0.5, etc. Rather than teach the students to count decimal points in the factors to place the decimal point in the product, I had my students relate the decimal expression to a basic fact, compare the size of the factors in the two, and then use that comparison to figure out the size of the product. For instance, if the students had to figure out the product of 0.3 and 9, they would start with 3 x 9 = 27, and since 0.3 is 1/10 the size of 3, the product of 0.3 x 9 would also be 1/10 the size of the product of 3 x 9. Since 2.7 is 1/10 the size of 27, then 0.3 x 9 = 27. We spent a great deal of time earlier in the year examining how the value of digits changed when shifted to the left and right in the place value system (e.g., when 4 shifts once to the right, it becomes 1/10 the size and when it shifts two times to the right, it becomes 1/100 the size, and so on), and we revisited this concept when learning the effect of multiplying decimals by powers of ten, so the thinking required by this approach came easily to most of the students. The cards in this set don’t require the use of any particular method, though, so you can use these cards with your students regardless of what strategy you’ve taught them for multiplying decimals.

The materials in this set allow for easy differentiation for your students’ needs. You may choose to use them as I did, having the students work with Set B1 first and then follow-up with Set B2. You may have some of your students work with Set B1 and others work with Set B2. You can even intermingle the two sets, mixing together some cards from Set B1 and some cards from Set B2. Perhaps you could have your students work on the odd cards from set B1 and the even cards from set B2, alternating between straightforward questions that simply require the calculation of a product and more challenging questions that require student to apply their decimal understanding. Since the two sets share one answer key (for example, the correct answer for Card 5 from Set B1 is “c”, and the correct answer for Card 5 from Set B2 is also “c”), you can mix the two sets together and still be able to accurately grade your students’ work.

There are lots of ways in which you can utilize these cards beyond the suggestions above. You can have the students work on them independently, solving the problems on the task cards on their own. The students can work on them in pairs or small groups, completing all the task cards in one or two sessions. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. The cards can even serve as a variation of “problem of the day”, with you 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**

The printables include two reference sheets that demonstrate concepts related to decimal and whole number multiplication and will be handy additions to your students’ math notebooks. The first reference sheet is a half-page and is designed in part to provide a springboard for discussion and journal writing. It presents sets of related multiplication equations and asks students to consider the similarities and differences among the equations in each set. I sized it so that it would fit on the top half of a journal page, leaving the bottom half for my students’ writing. The other reference sheet is the size of a full-sheet, and it illustrates the relationship between factors and products in whole number and decimal multiplication expressions. It provides examples of how someone might find the product of a decimal expression, such as 0.07 x 9, by using a basic fact – in this case, 7 x 9. Your students can use the journal inserts as a guide while they work on the cards, as well as when they complete other tasks that relate to multiplying decimals.

**Assessing Student Understanding**

The provided assessment activities can be used to evaluate your students’ mastery of the concept of multiplying decimals and whole numbers. The first four assessment activities are full-page in length and designed in pairs. The activities in each pair are formatted similarly, and have similar types of questions, though the numbers on each are different. The first two assessment activities (activities a and b) reflect the kinds of questions on the cards in set B1, requiring students to simply find the product of decimals and whole numbers and decimals and decimals. The second two assessment activities (c and d) reflect the kinds of questions on the cards in set B2, requiring students to be able to apply their understanding of decimal multiplication. All four activities require students to respond in writing to a prompt, and a rubric is included to help evaluate your students’ responses.

In addition to these four assessment pages, you also have four half-page, “exit ticket”-style assessments. Each of these exit tickets present students with a series of equations and ask them to write about the patterns evident in the equations.

You can use these activity pages in a variety of ways. You could give one or more as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give different activities as an independent post-test. You could also have the students work on the task cards, then complete one of the pages as guided practice with yourself, a partner, or a small group, and then give the second worksheet as an independent assessment. The activities could also be given as homework, center assignments, or any other purpose that fits your teaching style or classroom routines. With eight difference activities, you have enough for classwork, center work, homework, and then some!

For more practice with decimal concepts, please check out the other related resources I have available –

**Brainy Birds - x and ÷ with powers of ten task cards and printables (set a)**

Calc Trouble reasoning about decimal multiplication task cards + printables

Dog-Gone Decimals - rounding decimals task cards & printables (set a)

Dog-Gone Decimals – decimal estimation task cards & printables (set b)

Placing the Value - task cards + printables set

Grid Match-Up - relating tenths and hundredths game, activity cards, printables

On the Grid - modeling decimals and fractions task cards & printables (set a)

On the Grid - adding tenths and hundredths task cards & printables (set b)

I hope your students enjoy these resources and are able to build their proficiency with decimals. – Dennis McDonald

____________________________________________________________________

Common Core State Standards for Mathematics addressed:

• Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (5.NBT.7)

____________________________________________________________________

Included:

• 2 reference sheets

• 2 sets of 32 task cards

• task card answer sheet and key

• 8 self-checking “answer cards”

• 8 assessment activities

• rubric and answer key for assessment activities

This set of task cards is designed as a follow-up to Set A of my

This set of cards focuses on multiplying decimals by decimals and decimals by whole numbers. The highest place in the factors is the hundreds place, and none of the factors or products have digits any lower than the hundredths place. All of the factors have only one non-zero digit (for instance, 400, 7, 0.02, and 0.9), which allows students to be able to use basic facts to mentally multiply the factors.

There are two sets of 32 task cards, and the questions and answers on the two sets do not overlap. Each card in Set B1 presents students with a multiplication expression and simply requires students to find the product, while Set B2 has students apply their understanding of decimal multiplication to perform a variety of tasks, such as comparing expressions and identifying the value of a variable. Each set uses a different color border (blue for Set B1 and purple for Set B2). In addition, each card is labeled as belong to Set B1 or Set B2 to help distinguish them if you decide to print the cards in grayscale. [The simple graphics on each card look great in b & w or color!]

When I taught multiplication with decimals, I began with simple expressions like the ones on these cards: 0.3 x 8, 0.04 x 7, 0.9 x 0.5, etc. Rather than teach the students to count decimal points in the factors to place the decimal point in the product, I had my students relate the decimal expression to a basic fact, compare the size of the factors in the two, and then use that comparison to figure out the size of the product. For instance, if the students had to figure out the product of 0.3 and 9, they would start with 3 x 9 = 27, and since 0.3 is 1/10 the size of 3, the product of 0.3 x 9 would also be 1/10 the size of the product of 3 x 9. Since 2.7 is 1/10 the size of 27, then 0.3 x 9 = 27. We spent a great deal of time earlier in the year examining how the value of digits changed when shifted to the left and right in the place value system (e.g., when 4 shifts once to the right, it becomes 1/10 the size and when it shifts two times to the right, it becomes 1/100 the size, and so on), and we revisited this concept when learning the effect of multiplying decimals by powers of ten, so the thinking required by this approach came easily to most of the students. The cards in this set don’t require the use of any particular method, though, so you can use these cards with your students regardless of what strategy you’ve taught them for multiplying decimals.

The materials in this set allow for easy differentiation for your students’ needs. You may choose to use them as I did, having the students work with Set B1 first and then follow-up with Set B2. You may have some of your students work with Set B1 and others work with Set B2. You can even intermingle the two sets, mixing together some cards from Set B1 and some cards from Set B2. Perhaps you could have your students work on the odd cards from set B1 and the even cards from set B2, alternating between straightforward questions that simply require the calculation of a product and more challenging questions that require student to apply their decimal understanding. Since the two sets share one answer key (for example, the correct answer for Card 5 from Set B1 is “c”, and the correct answer for Card 5 from Set B2 is also “c”), you can mix the two sets together and still be able to accurately grade your students’ work.

There are lots of ways in which you can utilize these cards beyond the suggestions above. You can have the students work on them independently, solving the problems on the task cards on their own. The students can work on them in pairs or small groups, completing all the task cards in one or two sessions. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. The cards can even serve as a variation of “problem of the day”, with you giving each student 1 sheet of 4 cards to glue in their journals and solve, one sheet per day for eight days.

The printables include two reference sheets that demonstrate concepts related to decimal and whole number multiplication and will be handy additions to your students’ math notebooks. The first reference sheet is a half-page and is designed in part to provide a springboard for discussion and journal writing. It presents sets of related multiplication equations and asks students to consider the similarities and differences among the equations in each set. I sized it so that it would fit on the top half of a journal page, leaving the bottom half for my students’ writing. The other reference sheet is the size of a full-sheet, and it illustrates the relationship between factors and products in whole number and decimal multiplication expressions. It provides examples of how someone might find the product of a decimal expression, such as 0.07 x 9, by using a basic fact – in this case, 7 x 9. Your students can use the journal inserts as a guide while they work on the cards, as well as when they complete other tasks that relate to multiplying decimals.

The provided assessment activities can be used to evaluate your students’ mastery of the concept of multiplying decimals and whole numbers. The first four assessment activities are full-page in length and designed in pairs. The activities in each pair are formatted similarly, and have similar types of questions, though the numbers on each are different. The first two assessment activities (activities a and b) reflect the kinds of questions on the cards in set B1, requiring students to simply find the product of decimals and whole numbers and decimals and decimals. The second two assessment activities (c and d) reflect the kinds of questions on the cards in set B2, requiring students to be able to apply their understanding of decimal multiplication. All four activities require students to respond in writing to a prompt, and a rubric is included to help evaluate your students’ responses.

In addition to these four assessment pages, you also have four half-page, “exit ticket”-style assessments. Each of these exit tickets present students with a series of equations and ask them to write about the patterns evident in the equations.

You can use these activity pages in a variety of ways. You could give one or more as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give different activities as an independent post-test. You could also have the students work on the task cards, then complete one of the pages as guided practice with yourself, a partner, or a small group, and then give the second worksheet as an independent assessment. The activities could also be given as homework, center assignments, or any other purpose that fits your teaching style or classroom routines. With eight difference activities, you have enough for classwork, center work, homework, and then some!

For more practice with decimal concepts, please check out the other related resources I have available –

Calc Trouble reasoning about decimal multiplication task cards + printables

Dog-Gone Decimals - rounding decimals task cards & printables (set a)

Dog-Gone Decimals – decimal estimation task cards & printables (set b)

Placing the Value - task cards + printables set

Grid Match-Up - relating tenths and hundredths game, activity cards, printables

On the Grid - modeling decimals and fractions task cards & printables (set a)

On the Grid - adding tenths and hundredths task cards & printables (set b)

I hope your students enjoy these resources and are able to build their proficiency with decimals. – Dennis McDonald

Total Pages

36

Answer Key

Included with Rubric

Teaching Duration

N/A

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