Richland Parish School Board



Grade 3

Mathematics

Unit 2: Place Value and Number Representations

Time Frame: Approximately four weeks

Unit Description

The focus of this unit is the extension of place value concepts and the development of various representations for numbers including inequalities. Applying place value concepts to addition and subtraction is emphasized. Computational strategies including estimation, mental math, use of calculators, and use of paper/pencil are explored.

Student Understandings

Students develop an understanding of place value, comparing and ordering numbers, rounding, and adding and subtracting 3-digit numbers. Students apply appropriate strategies to a given situation and use them to solve problems.

Guiding Questions

1. Can students determine appropriate use of inequality symbols to compare numbers?

2. Can students round numbers to the nearest 10 and 100.

3. Can students use different strategies to solve addition and subtraction problems?

4. Can students add and subtract numbers of 3 digits or less?

5. Can students make informed choices about the appropriate use of problem-solving strategies?

6. Can students determine when and how to use computational strategies?

Grade 3 Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS)

|Grade Level Expectations |

|GLE # |GLE Text and Benchmarks |

|Number and Number Relations |

|2. |Read, write, compare, and order whole numbers through 9999 using symbols (i.e., ) and models (N-1-E) |

| |(N-3-E) |

|11. |Add and subtract numbers of 3 digits or less (N-6-E) (N-7-E) |

|13. |Determine when and how to estimate, and when and how to use mental math, calculators, or paper/pencil strategies |

| |to solve addition and subtraction problems (N-8-E) (N-9-E) |

|CCSS for Mathematical Content |

|CCSS # |CCSS Text |

|Numbers and Operations in Base Ten |

|3.NBT.1 |Use place value understanding to round whole numbers to the nearest 10 or 100. |

|ELA CCSS |

|CCSS # |CCSS Text |

|Writing Standards |

|W.3.2 |Write informative/explanatory texts to examine a topic and convey ideas and information clearly. |

Sample Activities

Activity 1: The Largest Number Game (GLE: 2)

Materials List: deck of cards with face cards removed, base-10 blocks or paper models of base-10 blocks, number cubes, paper, pencil, Place Value Chart BLM

Give pairs of students a deck of cards with face cards removed and have each student draw four cards. Have each student make a 4-digit number with his/her cards. Have students create and model the largest four-digit number with base-10 materials (i.e., base-10 blocks or paper models of base-10 blocks). Have students compare their numbers by comparing the base-10 block models. Have students read their numbers aloud to their partners. The student with the largest number keeps all eight cards played. Continue until all cards are used.

Variations:

(1) Use number words instead of numerals on the cards.

(2) Students can use place value charts with thousands, hundreds, tens, and ones labeled at the top of four columns to demonstrate their numbers before using the base-10 blocks to model the number.

(3) On a paper with the students’ names printed across the top, have each student in the pair write his/her number in standard form under his/her name. In the middle, one student writes the correct sign for comparing the numbers (< or >).

(4) Instead of using the highest number, use the lowest.

(5) Use number cubes instead of cards.

Activity 2: Somewhere Between (GLE: 2; CCSS: W.3.2)

Materials List: paper, pencil

Place students in groups of three. Have Student 1 write a four-digit number, Student 2 write a second four-digit number that is not consecutive to the number written by Student 1, and Student 3 write a number that is between the first two numbers. Have each student then write three statements using the numbers created and each of the inequality symbols (, and [pic]) at least once.

After the students have done this, have them create a text chain (view literacy strategy descriptions) using four-digit numbers and the words “greater than,” “less than,” and “unequal.” Students can share their stories at the conclusion of the lesson as a review of , and ≠. An example of a story chain might be as follows:

Student 1: I have 2,453 buttons. My number of buttons is greater than the number of buttons that (next student’s name goes here) has.

Student 2: I have 987 buttons. I have fewer buttons than (next student’s name goes here) has.

Student 3: I have 3,643 buttons. This number is unequal to the number of buttons that (student’s name goes here) has.

Activity 3: Four-Digit < and > (GLE: 2)

Materials List: paper, pencil

Have students work in pairs. Ask Student 1 to write a four-digit number and the symbol < or > with Student 2 completing the number sentence with a four-digit number. Continue the activity having the students alternate roles.

Extension: Have Student 1 write a four-digit number and the equal sign (=). Student 2 then completes the number sentence by writing the number in words or in expanded form.

Activity 4: Addition Properties (GLE: 11; CCSS: W.3.2)

Materials list: paper, pencil, board, counters

Tell students that they will be using the split-page notetaking (view literacy strategy descriptions) method. When using this method, a line is drawn down an 8 ½” by 11” lined paper about 2 ½” from the left margin. Big ideas or key words are written on the left side of the paper and facts or definitions and examples are written to the right. The page can be used as a study tool by folding it on the line or covering up one side of the page and using the information in the other column to recall the covered information. There is an example of what this looks like at the end of this activity.

Tell the students the following: If you know the fact 8 + 7, you also know the fact 7 + 8. Ask them to prove that this is true. They can use counters to prove that it is true. Tell students that there is a property in mathematics which states that changing the order in which numbers are added does not change the sum. Have students write “commutative property” on the left side of the paper, then describe what the property means and give an example on the right side of the paper.

Ask the students to add the following 6 + 8 + 2. Ask if anyone added 8 + 2 first. Tell them that the associative property of addition states that changing the way the addends are grouped does not change the sum. So they could add 6 + 8 first and get 14 and then add 2 to 14 to get 16. Or they could add 8 + 2 to get 10 and then add 6 to get 16. This means that (6 + 8) + 2 = 6 + (8 + 2). Have students write “associative property” on the left side of the paper, and then describe what the property means and give an example on the right side of the paper.

Ask the students how many students are in class today (e.g., 24 students). Say that no new students will join the class at any time this hour and no students will leave the class at any time this hour. Ask how many students will be in the class at the end of the hour (24). The number of students at the end of the hour could be represented by 24 + 0 = 24 or by 24 – 0 = 24. Tell students that this shows the addition property of zero and the subtraction property of zero. Have students write “zero property of addition” on the left side of the paper, and then describe what the property means and give an example on the right side of the paper. Have them do the same for the subtraction property of zero. Ask students what happens when zero is subtracted from a number. (The difference is that number.) Also, ask students what happens when a number is subtracted from itself. (The difference is always zero). Give pairs counters and have them demonstrate problems following these rules such as 7 – 0 = 0 or 7 – 7 = 0. Have students give their partners a problem which demonstrates one of these rules and have the partners state the rule. After the first student has modeled a rule, reverse the partners’ roles.

Have pairs of students switch papers and check their examples. These notes can then be used to study and refer to as students prepare for tests or quizzes.

Example of split-page notetaking:

Commutative Property Changing the order in which numbers are added does not

change the sum. 12 + 3 = 15 3 + 12 = 15

Activity 5: The Relationship Between Addition/Subtraction (GLE: 11)

Materials List: index cards, pencil

Explain to students that a fact family is a group of number sentences that use the same numbers. Tell students that fact families can be used to show how addition and subtraction are related. Model a few fact families. Have students create index cards of fact families after giving them three related numbers. Continue giving students 3 related numbers and have them write fact families. Give 3 numbers that are not related such as 6, 7, 14. See if students notice that these numbers do not make a fact family.

Example of Fact Family Cards

These cards can be collected and used in a center to study facts for those students that are not proficient.

Activity 6: Composing New Units (GLE: 11; CCSS: W.3.2)

Materials List: base-10 blocks, learning logs, pencils, Composing New Units BLM

Teacher Note: The Common Core State Standards use the terms composing and decomposing rather than regrouping. This is because ten ones are needed to compose or create a ten-unit and a ten-unit can be broken apart or decomposed into ten ones. It is important to begin to use this terminology during the transition and also to use strategies which help students understand that the standard algorithm is based on adding and subtracting of place values. Standard algorithms for addition and subtraction are not expected to be mastered until fourth grade. In this course, it is important that students are able to add and subtract numbers of 3-digits or less, but they should be allowed to use place value strategies when doing so.

Have students sit in a circle and ask a volunteer to use base-10 blocks to model the number 156. Have another volunteer model the number 128. Have students put the hundred blocks together. Ask how many hundreds they have now (2). Write the problem on the board and indicate to students that they are going to record what they see in the base-10 blocks in a different way, then write 200 as the first partial sum as shown below.

156

+ 128

---------

200 (1 hundred + 1 hundred = 2 hundred or 200)

Next, have volunteers put the ten rods together. Ask how many tens they have (7). Ask students how to write 7 tens as a number (70). Then record the sum of the tens as shown below:

156

+ 128

---------

200 ( 1 hundred + 1 hundred = 2 hundred or 200)

70 (5 tens + 2 tens is 7 tens or 70)

Next, have volunteers put the ones blocks together. Ask how many ones they have altogether and where they should write this in the problem. (14, write it under the 70). Ask students what 14 means in terms of tens and ones (1 ten and 4 ones) and lead them to understand that the 1 must be placed under other numbers which are in the tens place, and that the 4 must be entered in the ones place.

156

+ 128

---------

200 (1 hundred + 1 hundred = 2 hundred or 200)

70 (5 tens + 2 tens is 7 tens or 70)

14 (8 ones + 6 ones is 14 ones which is 1 ten and 4 ones)

Show students how to complete the problem by adding the partial sums.

156

+ 128

---------

200 (1 hundred + 1 hundred is 2 hundred or 200)

70 (5 tens + 2 tens is 7 tens or 70)

14 (8 ones + 6 ones is 14 ones which is 1 ten and 4 ones)

284 (2 hundred, 7 tens + 1 ten or 8 tens, 4 ones)

Point out to students that the ones were added to ones, tens were added to tens, and hundreds were added to hundreds. Make sure that students understand that this is done because addition is based on finding the sum of the numbers in each place value in the same way that the base-10 blocks were grouped together to determine how many ones, tens, and hundreds were in the sum.

Note that the process of finding partial sums by adding numbers in the same place starts on the left and goes to the right. This is natural for students as they read from left to write; however, some students may be comfortable in using the right-to-left process which is more aligned with the process used for the standard addition algorithm.

156

+ 128

---------

14 (8 ones + 6 ones is 14 ones)

70 (5 tens + 2 tens is 7 tens or 70)

200 (1 hundred + 1 hundred = 2 hundred or 200)

284 (2 hundred, 7 tens + 1 ten or 8 tens, 4 ones)

Note that students should not be forced to use the traditional algorithm. Some students may need to model each number using base-10 blocks. After they model the problem, students will need to group like units, compose new units as needed, and find the answer. Have students draw a picture of the base-10 model used to demonstrate understanding.

For example, a student might draw the following for the given problem. 156 + 128=

Here is the ten that was composed of the 10 ones which are crossed out.

The new ten was composed by removing ten ones and adding one bar.

156 █ │││││ ● ●●● There are 2 hundreds, 8 tens, and 4 ones, so the answer is 284.

128 █ │││

Introduce the standard algorithm to students as a method for recording some of their thoughts. Students should not be forced to use the algorithm.

156

+ 128

---------

Have students add 6 ones and 8 ones to get 14 ones. Remind them that 14 ones can be composed into 10 ones and 4 ones or 1 ten and 4 ones. To record this, the 1 ten should be placed in the tens column and the 4 ones should be placed in the ones column. Tell them that some people record it this way.

1

156

+ 128

---------

4

Tell them that others record it this way.

156

+ 128

----1-----

4

Have students then add the tens to get 8 tens and add the hundreds to get 2 hundreds.

It is important that information on various strategies is provided and that students are allowed to experiment with various methods to determine which method works best for them. Therefore, provide students with other problems. Make sure to include problems in which students must compose numbers in the ones place (e.g., 146 + 328), some in which students must compose numbers in the tens place (e.g., 146 + 382), and some in which students must compose numbers in the hundreds place (e.g., 941 + 328). Give some problems in which students must compose numbers in more than one place (e.g., 146 + 378). Make sure to monitor the students as they work the problems. Have students complete the Composing New Units BLM. Encourage students to try different strategies without forcing them to use the standard algorithm. After students have finished, check the BLM together and allow students to discuss their strategies.

Activity 7: Rounding Using Place Value (CCSS: 3.NBT.1)

Materials List: base-ten blocks, paper, pencil, board

Tell students that they are going to round a number to the nearest 10. Display the number 56. Ask students which digit is in the tens place (5). Underline the digit 5 in the number simply to help students remember to which place they are rounding. Have students represent the number 56 with base ten blocks or draw a picture using sticks for the tens and circles for the ones.

56 = ||||| OOOOO

O

Tell students that since they are rounding to the nearest ten, they have to think about which two tens 56 is between (6 tens or 60 and 5 tens or 50). Have students represent 60, 56, and 50.

60 = ||||| |

56 = ||||| OOOOO

O

50 = |||||

Ask students to which number of tens is 56 closer (6 tens or 60). Tell students that 56 rounds to 60.

Have students round the following numbers to the nearest 10: 32, 67, 81, 45, and 98.

• For the number 45, make sure that students see that 45 is halfway between 40 and 50. Tell them that mathematicians decided many years ago that if a number were halfway between, the number would round up to the larger number.

• For the number 98, students must see that the two tens that 98 is between are 10 tens or 100 and 9 tens or 90. 98 rounds to ten tens or 100.

Do the same type of questions for rounding 435 to the nearest hundred. Tell students that they are going to round a number to the nearest 100. Display the number 435. Ask students which digit is in the hundreds place (4). Underline the digit 4 in the number, simply to help students remember to which place they are rounding. Have students represent the number 435 with base ten blocks or draw a picture using squares for the hundreds, sticks for the tens and circles for the ones.

435 = ( ((( ||| OOOOO

Tell students that since they are rounding to the nearest hundred, they have to think about which two hundreds 435 is between (5 hundreds or 500 and 4 hundreds or 400). Have students represent 500, 435, and 400.

500 = (((((

435 = ( ((( ||| OOOOO

400 = ((((

Ask students which hundred is closer to 435 (4 hundreds or 400). Ask students how they know this. (Some may say 35 is less than 50; some may say that 335 is closer to 400 than 500.) Tell students that 435 rounds to 400.

Have students round the following numbers to the nearest 100: 385, 136, 290, 250, and 956.

• For the number 250, make sure that students see that 250 is halfway between 300 and 200, so it will round up to the larger hundred.

• For the number 956, students must see that the two hundreds that 956 is between are 10 hundreds or 1000 and 9 hundreds or 900. 956 rounds to ten hundreds or 1000.

Have students round 458 to the nearest hundred. (500). Have them round it to the nearest 10. (460) Give other examples where students first round a number to the nearest 100 and then to the nearest 10.

Activity 8: Rounding Using a Number Line (CCSS: 3.NBT.1)

Materials: paper, pencil, board, Rounding BLM

Tell students that drawing a number line can also help them round a number. Draw a number line on the board from 60-70 as shown in the example below. Show students the example:

Round each of the following numbers the nearest 10: 63, 68, and 65.

60 61 62 63 64 65 66 67 68 69 70

• Ask students which ten is 63 closer to, 6 tens (60) or 7 tens (70). (The answer is 60)

• Which ten is 68 closer to? (The answer is 70)

• Which ten 10 is 65 closer to? (Neither, but since it is halfway between the two numbers, it would round to 70.)

Show the example:

Round each of the following numbers to the nearest hundred.

400 410 420 430 440 450 460 470 480 490 500

• Ask students which hundred is 457 closer to, 4 hundreds (400) or 5 hundreds (500). (The answer is 500)

• Which hundred is 409 closer to? (The answer is 400)

• Which hundred is 450 closer to? (Neither, but since it is halfway between the two numbers, it would round to 500.)

Give students numbers and ask them to round the numbers to either the nearest 10 or to the nearest hundred. Have them sketch number lines to find the answers.

Ask the students to give examples of when rounding numbers might be helpful. For each example given, ask questions about whether rounding is indeed appropriate or if the example really requires an exact answer. If the students cannot give examples of when rounding is appropriate, tell them that rounding numbers is used when only a rough idea of an amount is needed.

The following are some examples:

• If bananas cost 39¢ a pound, about how much money would you need to buy two pounds? (39¢ is close to 40¢, so you know that you would need about $.80.)

• If the third grade classes were planning an end-of- the- year party, would three bags of cookies, each containing 20 cookies, be enough to give each student 2 cookies? Class A has 19 students, Class B has 23, and Class C has 26 students? (No, because there would be only 60 cookies and 17 rounds to 20, 23 rounds to 20, and 26 rounds to 30 and that sum rounds to 70. This total is greater than the 60 cookies from the three bags.)

• If a toy earned with tickets won at an arcade is 18 tickets and another toy is 11 tickets, about how many tickets will you need to buy the 2 prizes? (18 rounds to 20, and 23 rounds to 20, so you would need about 40 tickets.)

Tell students that rounding is very useful when performing addition and subtraction to check sums and differences. Example: 78 + 29 = 107 would round to 80 + 30 = 110. Rounding can help students determine if their answer is correct. For example, in the problem 78 + 29, if they had gotten an answer of 917, they would know that their answer was incorrect. Tell students that their actual sum or difference should be close to the sum or the difference of the estimated problem.

Have students complete the Rounding BLM and check it together. Students should show which method they used to round each number, drawing base-10 blocks or drawing a number line.

Activity 9: Subtraction by Counting Up (GLE: 11; CCSS: W.3.2)

Materials List: board, paper

Tell students that there are many ways to subtract.

Give students the following problem. The school librarian knows that she needs to have 327 books on the shelves for third grade students to have a good selection from which to read. She has counted and found that there are now 168 books available. You have been asked to find the number of books that she needs to purchase. Display the problem 327 – 168. Tell students that they can use a counting up strategy to find the answer to this problem. They should start with 168 and think about how much is needed to reach 327. It is always wise to try to get to multiples of 10 or 100.

Tell students to draw an open number line. An open number line is a number line where students place the numbers, and it is not divided into equal intervals. Have students draw a line and place 168 and 327 on it. (See the example below.) Have them decide what must be added to the smaller number to reach the next 10s number. In this example, they would add 2 to 168 to bring 168 up to 170. Write the +2 above the numbers. Have students determine what must be added to reach the next hundreds place. In this example, they would add 30 to 170 to get 200. Write +30 above the numbers. Have students determine what must be added to 200 to get to the next hundreds place. In this example, they would add 100. Write +100 above the numbers. Have students determine what must be added to find the total. In this example, they would add 27 to get to 327. Write +27 above the numbers. Have the students add 2, 30, 100, and 27 to get 159. 327 – 168 = 159.

+ 2 +30 +100 +27

168 170 200 300 327

There were 159 missing CDs.

Some students may choose to add 100 first, some may see that they could add 32 to 168 to get to 200, some may add 200 to 168 to get 368 and then subtract to get back to 327. Allow students to choose. Discussion is very important so that students can see different ways to use the counting up strategy.

Instruct students to draw an open number line to solve the subtraction problem 463 – 246. Allow different students to come to the board and draw their open number lines while other students check their own. Give students other numbers to subtract using the counting up strategy.

Have students create a RAFT writing (view literacy strategy descriptions) with the following information. A RAFT writing gives students a role, audience, form, and topic to use when writing. Use the following:

Role: tutor

Audience: friend

Form: letter

Topic: subtraction by counting up

Have students write a letter to a friend explaining how to subtract using the counting up method of subtraction. When students have completed their writings they can share them with a small group and check each other for accuracy. These letters can be used to study for a test or quiz. They can also be used for peer tutoring.

Activity 10: Subtraction Requiring Decomposition of Units (GLE: 11)

Materials List: base-10 blocks, learning log, pencil

Write the problem 154 – 36 = ? on the board. Have students work the problem using the counting up strategy. Have a few students explain how they subtracted. Tell them that there are other strategies that could be used to find the answer to this problem.

Have students model 154 using base-10 blocks. As they model the number, draw a picture of 154 using a square for the hundreds, sticks for the tens, and circles for the ones.

154 = ( ||||| OOOO

Have students think about how they could remove 36 of the blocks. They should see that they do not have enough of the ones blocks to remove 6 ones blocks. (Some students may go ahead and remove 3 tens. This is okay.) Ask them what they could do to subtract 6 ones from 4 ones. Lead them to the idea that they could decompose one of the tens into 10 ones. If they do this, ask them what they now have showing (1 hundred block, 4 tens and 14 ones).

Show this using the drawing model.

154 = ( |||| OOOOO

OOOOO

OOOO

Students can now remove 36 blocks from the 154 blocks now shown as 100 + 40 + 14. The result is 118. This method involves taking away the 36 from 154.

Another way to solve the problem is to have students determine how much larger one number is than the other. Tell students that they can make a picture of their problem to help them regroup. Remind them that the square represents the hundreds, the sticks represent the five tens, and the circles represent the ones.

Example:

154

36

Remind students that they can subtract by removing equivalent units from each number. Have students notice that 36 has more ones than 154, so removing the same number of units will require decomposing a ten in 154 into ten ones.

Begin with the picture of 154 above and change it to the one below.

154

Ask students if the amount has changed. (No, the model still shows 154, but now it shows 100 + 40 + 14.) Show students that they have enough ones to subtract the ones place. They should subtract 6 ones from 14 ones to get 8 ones. Have them finish the problem.

154

36

154

- 36

118

This method involves comparing the 2 amounts and finding the difference.

Review the steps of subtraction with decomposing numbers.

Step 1: Draw each number with base-10 blocks or show just one of the numbers.

Step 2: Subtract the ones and decompose a set of tens, if necessary.

Step 2: Subtract the tens and decompose a set of hundreds, if necessary.

Step 3: Subtract the hundreds.

Have students work in pairs to model the number 243. Ask students to subtract 125 blocks to see what is left. As students begin to see that they cannot take 5 ones away from 3 ones, remind

them of the idea of decomposing. Show them that they can take one rod and trade it for 10 ones. Have students trade one of their rods for ten ones and put the 10 ones with the 3 ones that they already have.

243

- 125

------- Begin with the picture above and change it to the one below.

Guide students to realize that decomposing a ten into 10 ones enabled them to do this. They replaced a 10-stick for 10 ones. The number 243 is now represented by 2 hundreds, 3 tens, and 13 ones. To subtract 125, five ones, 2 tens, and 1 hundred can now be deleted as shown below.

The number remaining is now 118. 243 – 125 = 118.

Have students do the same problem by using the idea of comparing the 2 amounts and finding the difference and by using a number line to find the difference.

Tie the problem above to the standard algorithm. Again, students should not be forced to use the algorithm.

243

- 125

-------

Tell students that in order to subtract 5 ones from 3 ones, one of the tens must be decomposed into 10 ones. There will now be 2 hundreds, 3 tens, and 13 ones. Tell them that some people record 2 hundreds, 3 tens, and 13 ones this way.

3 13

243

- 125

-------

Have students subtract 1 hundred, 2 tens, and 5 ones from 2 hundreds, 3 tens, and 13 ones.

Give the class other subtraction problems and have them draw pictures using the process of decomposing as needed until they have a true understanding of what decomposing a unit means. Be sure to give problems in which one hundred must be decomposed into 10 tens. Monitor work closely to ensure that students are using the correct process.

Another strategy when subtracting is for students to round the subtrahend to the next multiple of 10 and then compensate when finding the answer. For example:

156 could be worked as 156

-128 - 130

26

To get the correct answer, 2 must be added to 26 because 130 is 2 more than should have been subtracted. Therefore, the answer is 28.

Give students a few problems to work in their learning logs (view literacy strategy descriptions) to refer to as a study aid for a test or quiz. Each entry should indicate which strategy was used and provide the answer to the problem. When using the base-10 block strategy, students should show how to represent the number(s) using base-10 blocks and show the “subtraction” by either marking off matching units in each number or by showing the amount that was removed. They should also show the answer. If using the counting up method, they should show what they have done on a number line.

Activity 11: Subtracting Numbers with Zeros (GLE: 11)

Materials List: board, notebooks, Subtraction Problems BLM

Write the problem 304 – 43 = ? on the board. Ask students to draw a picture of the number 304 by drawing squares for the hundreds, sticks for the tens, and circles for the ones.

Example:

304

Have students discuss how they could subtract 43 from 304. Do they see any problems? (They should recognize that they need to subtract 4 tens and there are 0 tens in the tens place.) Remind students that in the number 304, there are 0 tens in the tens place but that there are 30 tens in the number. Ask students what they think they could do.

Students should see that they can decompose one hundred into 10 tens.

304 =

304 = 3 hundreds + 4 ones or 2 hundreds + 10 tens + 4 ones.

Have students remove the 43.

Subtract 43 by crossing out 4 sticks and 3 circles. Now there are 2 squares, 6 sticks, and 1 circle left. This represents the difference which is 261. Ask students to show how they could subtract these 2 numbers by using the compare method or by counting up using a number line.

Have students write the following problems in their notebooks and solve them with partners. 703 – 426 = 277 504 – 237 = 297 300 – 75 = 225

Have students to complete the Subtraction Problems BLM. Monitor students as they work.

Activity 12: Which Method of Computation Is Better? (GLEs: 2, 11, 13)

Materials List: calculator, paper, pencil, number cube

Have students complete an SQPL (view literacy strategy descriptions) by giving them the prompt, “In solving math problems, it is always easier or faster to use the calculator than to use other methods to solve the problems.” SQPL stands for Student Questions for Purposeful Learning. A statement is made and students think of questions about the statement. Questions should be written on the board. Star questions asked by more than one student. The following are some examples of questions students may ask: Is mental math a good option for large numbers? When would a calculator really help? Is it quicker to use mental math? Under what circumstances would using mental math be a good choice? a calculator? paper/pencil?

Have pairs of students use a calculator to create a three-digit number using three different digits. Have them first determine which number is larger by using their knowledge of place value. Next, ask students to write down their estimates of the difference between the two numbers. Before calculating the actual difference, each student will roll a number cube to determine his/her calculation method: 1 or 2 means the student must use mental math, 3 or 4 means a calculator must be used, and 5 or 6 means paper/pencil must be used. After the calculation method has been determined for each student, have students compare numbers (to determine how much larger one number is than the other) by subtracting the smaller number from the larger number using the pre-determined techniques.

As students work through this activity, they should refer to the SQPL and record answers to their questions in a notebook. After the activity, these answers can be used to review strategies and to help determine when it is best to use each one.

Variations:

1. Students add (instead of subtract) the numbers.

2. To practice calculator skills and writing numbers in different forms, have students in pairs use a calculator to create a four-digit number using four different digits. Ask students to trade calculators, with each student writing the number shown in word and/or expanded form.

Activity 13: And the Answer is…! (GLEs: 11, 13; CCSS: W.3.2)

Materials List: place cards for game, 3 bells, paper, pencil, vis-à-vis marker, small white boards, erasers, learning logs

Arrange the front of the classroom to look like a game show. Make three place cards to put in front of each group labeled “Mental Math,” “Pencil and Paper,” and “Calculator.” Assign two members to a group and have them sit in the front of the room by their cards. Give each group a small white board, a marker, and an eraser. Tell students that they must solve the problems given using only the strategy assigned to their group. The Mental Math group can only write the answer down on its board. The Calculator group must do the entire problem using the calculator and can only write the answer on its board when the final answer appears on the calculator. The Pencil and Paper group must write the entire problem down before they can write the answer. Each group also has a bell to ring when it has written the answer down.

Write an addition or subtraction problem that includes up to three digits. When students have finished their problems, check their answers and discuss their strategies. Why did the mental math group finish first? Why were pencil and paper quicker than using a calculator? Etc.

Read the problems and display them one at a time. Have students who are not contestants choose any strategy and solve the problems at their desks while contestants work on problems. Have a scorekeeper record the number of correct responses given first from each strategy group.

Choose questions that can easily be answered using the strategies suggested. Include questions that involve two-step word problems to show that these strategies can be used with word problems and in our daily lives. Help students see that there are situations when mental math is a better strategy than using a calculator, and there are situations when a calculator is a good choice.

Some possible situations:

• Estimate the sum of 410 and 523.

• What is the difference between 4520 and 3215?

• If I have 4 quarters, 3 dimes and 6 pennies, how much money do I have?

• The temperature this morning was 76 degrees. Last night’s low was 56. What is the difference in the 2 temperatures?

• 65 third graders ate lunch today and 74 ate lunch yesterday. What is the total number who ate lunch in the 2 days?

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In groups, have students discuss the types of problems that were easily solved with each strategy. Share the results with the class. Ask students to list some additional problems that could be solved easily with each strategy and to justify their responses in learning logs (view literacy strategy descriptions). These should include several statements about each of the strategies and when they think they will use each. These can be read and reviewed before a test or quiz for review.

Activity 14: Make It Real (GLEs: 11, 13)

Materials List: paper, pencil, calculator, Make It Real BLM

To help students practice estimation skills, attempt different calculation techniques, know when an estimate is appropriate, and know when an exact answer is needed, use real-world problems that involve the addition and/or subtraction of numbers up to 1000. The students should first be required to decide which operation to use and then decide if exact answers are required.

Problems might include phrases such as, “about how many,” in order to facilitate use of estimation skills. For example, an exact answer is needed when checking to see if the amount of change a teller returns is correct; however, an estimate would suffice for determining about how much money would be left out of $100 if $47 is spent. Tell students to complete the Make It Real BLM monitoring students as they work.

When modeling problems for students, think aloud about the choices available to solve the problem (using a calculator, using paper/pencil, drawing pictures or using base-10 blocks, or using a mental strategy). For example, determining the cost of a pack of paper priced at $0.60 and an eraser priced at $0.10 is an easy mental problem. Adding the cost of all the school supplies purchased by the class, however, is a problem in which using a calculator makes sense because of the amount of data.

Activity 15: Number Cards (GLEs: 2, 11; CCSS: W.3.2)

Materials: index cards (one per student), pencils

Give each student an index card on which a modified vocabulary card will be made. A vocabulary card (view literacy strategy descriptions) is a card made by the student that has the vocabulary word written in the middle. In the corners, a definition, the characteristics, an example, and an illustration of the term would be written. The card can be used to study vocabulary terms. On the modified vocabulary card for this activity, have students write a 4-digit number in the center of the card. In the first corner, have students write an addition problem in which the number in the middle of the card is the sum. In the second corner have, students write a subtraction problem in which the number in the middle of the card is the difference. In the third corner, have students write 2 inequalities using the > sign with the number on the card used first. In the last corner, have students write 2 inequalities using the < sign with the number on the card used first. Have students label each section of the card as shown on the example below. Two students can get together and check each other’s cards for accuracy. These cards will provide a review of addition, subtraction, and comparison of numbers.

Example:

Sample Assessments

General Guidelines

Students need to be observed both as individuals and in groups. Continue to assess students by listening to them during whole class and partner discussions.

General Assessment

• Include in the portfolio assessment the following:

✓ Anecdotal notes from teacher observation

✓ Student explanations from specific activities

✓ Learning log entries

• Set up performance tasks using number cards. Students will complete the activity creating the highest and lowest numbers and write about what they did.

• Ask students to explain how to add and subtract three digit numbers as if they were telling a friend. They may write this in their learning logs (view literacy strategy descriptions) with an example of an addition problem and a subtraction problem.

• Ask probing questions while students are working in groups such as:

✓ Do you understand what ____ is saying?

✓ What would happen if…?

• Provide sharing time for group work. Ask questions such as:

✓ Does anyone have another way to explain that?

✓ What do you think about that?

Activity-Specific Assessment

• Activity 3: Have students fill in the last number when given the first number and the inequality sign by the teacher. Ex: 6,876 >___?

• Activity 8: Provide students with advertisements or catalogs (for items like toys, groceries, or small appliances, etc.). Have students choose two (three, four . . .) items, and use rounding to estimate if they have enough of a given amount of money ($100, $200. . . $900) to “purchase” the items. Observe that students are rounding and not using paper and pencil to find an exact amount.

• Activity 10: Provide students with an index card and have them complete one subtraction problem with decomposing in the ones place on the front and one subtraction problem with decomposing in the tens place on the back. Allow students to use any strategy that works. They should not be required to use the algorithm.

Example:

Front Back

• Activity 13: Have students write one example problem for each of the different calculation methods - paper/pencil, mental math, calculators.

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9 8 17

Addition

8 + 9 = 17

Addition

9 + 8 = 17

Subtraction

17 – 8 = 9

Subtraction

17 – 9 = 8

Addition

5,002 + 262 =

Subtraction

5,414 – 150 =

5,264

Greater Than

5,264 > 4,299

5,264 > 5,168

Less Than

5,264 < 5,421

5,264 < 5,272

562 – 347 = 215

328 – 152 = 176

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