Base Ten BlocksBase Ten Blocks can be used to— model place value through 9,999 explore addition...

Base Ten Blocks A Guide to Teaching Strategies,

Activities, and Ideas

InTroduCTIon

2

This Learning About® Base Ten Blocks Activity Guide provides hands-on activities and ideas that allow you to lead students in an active exploration of the world of mathematics. The activities presented involve students in exploration of abstract concepts through the use of manipulatives. Students are encouraged to think critically, plan strategy, and share conclusions.

The Learning About® Base Ten Blocks Activity Guide emphasizes— ■■ communication■■ exploration■■ problem solving■■ analysis

Base Ten Blocks are available in wood, plastic, or ManipuLite®. The sets of Base Ten Blocks depict place value relationships between

Units (ones) 1 cm x 1 cm x 1 cm,Rods (tens) 1 cm x 1 cm x 10 cm,Flats (hundreds) 1 cm x 10 cm x 10 cm, andCubes (thousands) 10 cm x 10 cm x 10 cm.

Base Ten Blocks can be used to—

■■ model place value through 9,999■■ explore addition and subtraction■■ model regrouping

Exploring with Base Ten BlocksStudents at all grade levels should be allowed time to freely explore and experiment with Base Ten Blocks before guided activities begin.Group Size: Pairs or small groups

Materials:1 Flat (hundreds) 10 Rods (tens)10 Units (ones) crayons and pencils

paper

Procedure: Begin by questioning students about the similarities and differences among the different blocks. Have students compare a Unit to a Rod and a Rod to a Flat. Encourage students to verbalize their findings and discoveries. Ask one student to place a Rod on a piece of paper. The partner then places 10 Units next to the Rod. Both students should trace around the Rod and Units and color in the tracings. Lead a discussion of the place value relationship between the Rod and the Units.

InTroduCInG BASE TEn BLoCkS

■■ How many Rods (tens) did you trace? [1 Rod]■■ How many Units did you place next to the Rod? [10 Units]

Repeat this procedure using 1 Flat and 10 Rods. Continue to question students about the relationships they are uncovering among the Units, Rods, and Flats.

Group Size: Pairs or small groups

Materials:10 Rods (tens)10 Units (ones)

Procedure: Allow students a few minutes to freely explore the blocks. Review the names of the Unit and Rod blocks.

Have students answer the following questions using Base Ten Blocks. As students answer your questions, model their responses on the following Place Value Chart.

■■ Which block shows 1? [Unit]■■ Where would you place this block on the Place Value Chart? [Unitscolumn]

■■ Model the number 2 using the blocks. [2 Units]■■ Where would you place these blocks on the Place Value Chart?[Units column]

Continue this activity through the number 9.

■■ Model the number 10 using the blocks. [Some students may use 1Rod, others may choose to use 10 Units.]

■■ Explain how you modeled the number 10. [Answers will vary.]■■ What is the fast way to model the number 10? [Use 1 Rod.]

Cubes Flats Rods Units

3

ExPLorInG onES And TEnS PLACE vALuE

Write the following place value statement on the board:

10 is __ ten(s) and __ one(s).

Invite student volunteers to fill in the Place Value Chart on the board and the place value statement.

Continue this activity through the number 19.

Sample Responses:

[11 is 1 ten and 1 ones][15 is 1 ten and 5 ones][18 is 1 ten and 8 ones]


Materials:1 Place Value Chart10 Rods (tens)10 Units (ones)

Procedure: Allow students a few minutes to freely explore the blocks. Review the names of the Unit and Rod blocks. Encourage discussion of the relationships among the Base Ten Blocks.

■ How many Units will equal the value of 1 Rod? [10 Units]

Draw the Place Value Chart from page 3 on the board. Provide a copy of this Place Value Chart to each group of students.

■ Place 2 Rods and 4 Units on the Place Value Chart.■ What number is shown in the Rods column? [20]■ What number is shown in the Units column? [4]■ What have you modeled? [2 tens and 4 ones]■ What is another way you can name this number? [20 + 4 or 24]■ Place 4 Rods and 6 Units on the Place Value Chart.■ What number is shown in the Rods column? [40]■ What number is shown in the Units column? [6]■ What have you modeled? [4 tens and 6 ones]■ What is another way you can name this number? [40 + 6 or 46]

Continue this procedure for the numbers 53, 67, 79, 81, and 96.

Have students model the number 49 on their Place Value Charts.

■ How many Rods did you use? [4 Rods]■ How many Units did you use? [9 Units]

4

dEvELoPInG PLACE vALuE ThrouGh 99

5

Direct students to add one more Unit to their Place Value Charts.

■■ What is displayed now? [4 Rods and 10 Units]■■ What number does this model? [40 + 10 or 50]■■ What is another way to model the number 50? [5 Rods]

Encourage students to discuss how they traded 4 Rods and 10 Units for 5 Rods. [The 10 Units were exchanged for 1 Rod.]

Continue this activity for the numbers 39, 59, 69, 79, and 89. Ask students to build the number; then have students add one more Unit. Encourage students to explain how and why they exchanged 10 Units for 1 Rod.


Materials:1 Place Value Chart1 Flat (hundreds)10 Rods (tens)10 Units (ones)

Procedure: Allow students a few minutes to freely explore the blocks. Review the names and values of the Unit and Rod blocks.

Introduce the name and value of the Flat. Encourage discussion of the relationships among the Base Ten Blocks. Let students discover how many Rods equal 1 Flat by placing Rods on top of the Flat. Then challenge students to find how many Units equal 1 Flat.

■■ How many Units equal the value of 1 Rod? [10 Units]■■ How many Rods equal the value of 1 Flat? [10 Rods]■■ How many Units equal the value of 1 Flat? [100 Rods]

Draw the Place Value Chart from page 3 on the board. Provide a copy of this Place Value Chart to each group.

Direct students to place 9 Rods and 9 Units on their Place Value Charts.

■ What number is shown in the Rods column? [90]■ What number is shown in the Units column? [9]

■■ What have you modeled? [9 tens and 9 ones]■■ What is another way you can name this number? [90 + 9 or 99]

Have students add one more Unit to their Place Value Charts.

■■ What do you display now? [9 Rods and 10 Units]■■ What can be exchanged? [10 Units for 1 Rod]

dEvELoPInG PLACE vALuEThrouGh 999

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■ What do you have now? [10 Rods, 0 Units]■ What can be exchanged? [10 Rods for 1 Flat]■ What number does this show? [100]


■ What did you display?Sample responses:[1 Flat, 4 Rods, 6 Units][1 Flat, 0 Rods, 46 Units][0 Flats, 14 Rods, 6 Units]

■ What is the quickest, most efficient way to model the number 146?[1 Flat, 4 Rods, 6 Units]

Write the following chart on the board. Do not fill in the answers; place blank lines instead. Have students model numbers the quickest, most efficient way on their Place Value Charts. As students provide modeling solutions, fill in the chart on the board.

429 is [4] hundreds, [2] tens, [9] ones; or [4] Flats, [2] Rods, [9] Units320 is [3] hundreds, [2] tens, [0] ones; or [3] Flats, [2] Rods, [0] Units927 is [9] hundreds, [2] tens, [7] ones; or [9] Flats, [2] Rods, [7] Units103 is [1] hundred, [0] tens, [3] ones; or [1] Flat, [0] Rods, [3] Units


Materials: 1 Place Value Chart1 Cube (thousands)10 Flats (hundreds)10 Rods (tens)10 Units (ones)

Procedure: Allow students a few minutes to freely explore the blocks. Review the names and values of the Unit, Rod, and Flat blocks.

Introduce the name and value of the Cube. Encourage discussion of the relationships among the Base Ten Blocks. Invite student volunteers to model the relationship between 1 Cube and 10 Flats.

■■ How many Flats equal the value of 1 Cube? [10 Flats]

dEvELoPInG PLACE vALuEThrouGh 9,999

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Draw the Place Value Chart from page 3 on the board. Provide a copy of the Place Value Chart to each group of students. Direct students to place 9 Flats on their desks.

■■ What number have you modeled? [900]

Have students add one more Flat to their Place Value Charts.

■■ Now how many Flats are modeled? [10 Flats]■■ What can be traded? [10 Flats for 1 Cube]■■ What number does this show? [1,000]

Have students build the number 999 using the Base Ten Blocks.

■■ What blocks do you display? [9 Flats, 9 Rods, 9 Units]

Have students add one more Unit to their models.

Invite students to exchange Base Ten Blocks to build the quickest, most efficient model for this number.

■■ 10 Units can be exchanged for 1 Rod.■■ 10 Rods can be exchanged for 1 Flat.■■ 10 Flats can be exchanged for 1 Cube.■■ What number have you modeled? [1,000]

Write the following place value sentence on the board. Do not fill in the answers; place a blank line instead. Have students model the place value sentence on their Place Value Charts.

1,000 is [1] thousand, [0] hundreds, [0] tens, [0] ones.

Write the following chart on the board. Do not fill in the answers; place blank lines instead. Direct students to build the following numbers on their Place Value Charts in the quickest, most efficient way.

3,000 is [3] thousands, [0] hundreds, [0] tens, [0] ones.2,945 is [2] thousands, [9] hundreds, [4] tens, [5] ones.7,463 is [7] thousands, [4] hundreds, [6] tens, [3] ones.9,999 is [9] thousands, [9] hundreds, [9] tens, [9] ones.

Group Size: Pairs or Small Groups


Procedure: Review the names of the Unit and Rod blocks. Invite discussion of the relationships among the Base Ten Blocks.

AddInG TEnS

8

■■ ■How many Units equal the value of 1 Rod? [10 Units]

Have students model the following values at their desks.

■■ Place 1 Rod on your desk.■■ What number is modeled? [10, or 1 ten]■■ Place another Rod under the first Rod.■■ What number do the 2 Rods model? [20, or 2 tens]

Write the following on the board:

10 1 ten +10 + 1 ten20 2 tens

Direct students to model the following values using the Rods.

■■ Place 4 Rods on your desk.■■ What number is modeled? [40, or 4 tens]■■ Place 3 more Rods under the first Rods.■■ What number do the 4 Rods plus 3 Rods model? [70, or 7 tens]

Write the following on the board: 40 4 tens

+30 +3 tens70 7 tens

Have students find the following sums using Rods.

2 tens + 3 tens = [5 tens, or 50]6 tens + 2 tens = [8 tens, or 80]4 tens + 4 tens = [8 tens, or 80]1 ten + 5 tens = [6 tens, or 60]3 tens + 6 tens = [9 tens, or 90]



Procedure: Allow students a few minutes to explore the Base Ten Blocks. Have students model the following numbers in the quickest, most efficient way: 5, 14, 21, 36, and 79.

Review the addition of sums of tens. Have students model the addition of 30 plus 40.

AddInG Two-dIGIT nuMBErS wIThouT rEGrouPInG

9

3 tens 30+4 tens +40

7 tens 70

Direct students to model the number 31.

■ How many Units did you use? [1 Unit]■ How many Rods did you use? [3 Rods]

Have students model the number 12 below the 31.

■ How many Units did you use? [2 Units]■ How many Rods did you use? [1 Rod]■ Add 31 and 12.■ Always add the ones first.■ How many ones are there? [3 ones]■ Add the tens next.■ How many tens are there? [4 tens]■ How much is 31 plus 12? [4 tens and 3 ones, or 43]

Write the following on the board. Invite student volunteers to solve the addition.

tens ones3 1 31

+1 +2 +124 3 43

Continue this procedure for the following addends:

21 + 14 = [3 tens and 5 ones, or 35]16 + 22 = [3 tens and 8 ones, or 38]42 + 17 = [5 tens and 9 ones, or 59]36 + 22 = [5 tens and 8 ones, or 58]

Extend this activity by having one student in each group solve the following addition problems using paper and pencil or mental arithmetic. Another student in the group should check the problem using Base Ten Blocks.

33 26 14 28 71+11 +10 +23 +31 +13[44] [36] [37] [59] [84]

10


Materials:1 Place Value Chart10 Flats (hundreds)20 Rods (tens)20 Units (ones)

Procedure: Allow students a few minutes to explore the relationships among the blocks.

Draw the Place Value Chart from page 3 on the board. Provide a copy of the Place Value Chart for each group of students.

Have students place 13 Units on their Place Value Charts.

■■ How many Units do you have? [13 Units]■■ How many Units can be exchanged for a Rod? [10 Units]

Direct students to conduct this exchange on their charts.

■■ How many Rods do you have now? [1 Rod]■■ How many Units do you have now? [3 Units]■■ What number have you modeled? [13]

Introduce the term regroup and write the following on the board:

13 ones = 1 ten and 3 ones13 ones are regrouped as 1 ten and 3 ones.

Repeat this procedure for the following numbers:

16 ones = [1 ten and 6 ones, or 16]14 ones = [1 ten and 4 ones, or 14]19 ones = [1 ten and 9 ones, or 19]

Have students place 11 Rods on their Place Value Charts.

■■ How many Units do you have? [none]■■ How many Rods do you have? [11 Rods]■■ How many Rods can be exchanged for a Flat? [10 Rods]

Direct students to conduct this exchange on their charts.

■■ How many Flats do you have now? [1 Flat]■■ How many Rods do you have now? [1 Rod]■■ How many Units do you have now? [none]■■ What number have you modeled? [110]

rEGrouPInG onES, TEnS, And hundrEdS

11

Write the following on the board:11 rods = 1 Flat, 1 rod, 0 units11 tens are regrouped as 1 hundred, 1 ten, 0 ones

Repeat this procedure for the following numbers:

14 Rods = [1 hundred, 4 tens, and 0 ones; or 140] 18 Rods = [1 hundred, 8 tens, and 0 ones; or 180]

20 Rods = [2 hundreds, 0 tens, and 0 ones; or 200]

Continue this activity. One student in each group will build the model on the Place Value Chart. Another student in each group will conduct the regrouping and record the results. (If there are more than two students in a group, the role of “Recorder” can be assigned to a third student.)

2 tens, 13 ones = [3 tens and 3 ones, or 33]5 tens, 10 ones = [6 tens and 0 ones, or 60]1 ten, 12 ones = [2 tens and 2 ones, or 22]14 tens, 3 ones = [1 hundred, 4 tens, and 3 ones; or 143]16 tens, 8 ones = [1 hundred, 6 tens, and 8 ones; or 168]20 tens, 3 ones = [2 hundreds, 0 tens, and 3 ones; or 203]

Challenge your students with the following regrouping problems.

11 tens, 16 ones = [1 hundred, 2 tens, and 6 ones; or 126]14 tens, 19 ones = [1 hundred, 5 tens, and 9 ones; or 159]20 tens, 13 ones = [2 hundreds, 1 ten, and 3 ones; or 213]18 tens, 14 ones = [1 hundred, 9 tens, and 4 ones; or 194]



Procedure: Allow students a few minutes to explore the blocks.


AddInG Two-dIGIT nuMBErS wITh rEGrouPInG

12

Review exchanging and regrouping of 10 Units for 1 Rod. Have students model the following regroupings on their Place Value Charts.

14 ones [1 ten and 4 ones, or 14]18 ones [1 ten and 8 ones, or 18]

21 ones [2 tens and 1 one, or 21]


■■ How many ones do you have? [3 ones]■■ How many tens do you have? [1 ten]

Direct students to model the number 19 under the 13 on their Place Value Charts.

■■ The number 19 has how many ones? [9 ones]■■ The number 19 has how many tens? [1 ten]■■ Now add 13 + 19.■■ Add the ones together first. How many ones are there? [12 ones]■■ Are there more than 10 ones? [yes]■■ Exchange 10 ones for 1 ten.■■ Now add the tens together. How many tens are there? [3 tens]

Draw the following chart on the board. Invite student volunteers to explain the addition, exchanging, and regrouping process.

tens ones

1 3 13+1 +9 +19

32

■■ Add the ones first.3 ones + 9 ones = 12 ones12 ones = 1 ten and 2 ones

■■ Write the 2 ones in the ones column, regroup the 1 ten in the tenscolumn.

■■ Add the tens.1 ten + 1 ten + 1 ten = 3 tens13 + 19 = 3 tens and 2 ones or 32

Continue this procedure for the following addition sentences: 14 + 27 = [41]36 + 49 = [85]22 + 19 = [41]25 + 18 = [43]

1

13


Materials:

1 Place Value Chart20 Rods (tens)20 Units (ones)

Procedure: Allow students a few minutes to explore the blocks.



■ How many ones do you have? [9 ones]■ How many tens do you have? [1 ten]

Direct students to model the number 11 under the number 19 on their Place Value Charts.

■ The number 11 has how many ones? [1 one]■ The number 11 has how many tens? [1 ten]■ Now subtract 11 from 19. Subtract the ones first.■ 9 ones minus 1 one equals? [8 ones]■ 1 ten minus 1 ten equals? [0 tens]■ How much is 19 – 11? [8 ones, or 8]

Draw the Place Value Chart from page 3 on the board. Question students as to the process they use to solve the subtraction.

tens ones

1 9 19–1 –1 –110 8 8

Continue this procedure for the following subtraction sentences.

18 – 10 = [8]17 – 14 = [3]25 – 11 = [14]39 – 16 = [23]

SuBTrACTInG Two-dIGIT nuMBErSwIThouT rEGrouPInG

12

14



Procedure: Allow students a few minutes to review the value relationships between the Rods and Units.

Review exchanging and regrouping 10 Units for 1 Rod. Have students model the following exchanges and regrouping on their Place Value Charts.

16 ones [1 ten and 6 ones, or 16]24 ones [2 tens and 4 ones, or 24]18 ones [1 ten and 8 ones, or 18]27 ones [2 tens and 7 ones, or 27]


Have students model the number 35 on their Place Value Charts. Direct students to model the number 18 under the 35 on their charts. Write the following on the board:

35–18

■■ Start with the ones. How many ones are there in the number 35?[5 ones]

■■ How many ones are there in the number 18? [8 ones]■■ Can you subtract 8 ones from 5 ones? [No, at this level a larger numbercannot be subtracted from a smaller number.]

■■ We need to exchange and regroup the blocks to solve this problem.■■ Regroup the 3 tens, 5 ones of the number 35 as 2 tens, 15 ones.

Now continue the subtraction.

■■ Subtract the ones first. 15 ones minus 8 ones equals 7 ones.■■ Subtract the tens next. 2 tens minus 1 ten equals 1 ten.

35 – 18 = 1 ten and 7 ones, or 17

SuBTrACTInG Two-dIGIT nuMBErSwITh rEGrouPInG

15

Write the following on the board. Invite students to explain the exchanging and regrouping needed to solve this subtraction problem.

tens ones tens ones3 5 2 15

–1 –8 –1 –81 7 1 7

Continue this procedure for the following subtraction sentences: 36 – 18 = [18]21 – 15 = [6]24 – 15 = [9]47 – 19 = [28]

Super Source® BaSe Ten BlockS Teacher reSource BookS

■■ Each Super Source Book is a classroom-tested way to implement ahands-on learning approach to mathematics as recommended in theNCTM Standards! The comprehensive three-step lesson plans makedeveloping day-to-day lessons easy and fun.

The Super Source BaSe Ten BlockS kiT

■■ Provide students with activities that develop the understanding ofnumber sense, computation, place value, and measurement. Kitcontains a Super Source Teacher Resource Book, one set of OverheadBase Ten Blocks, and enough Base Ten Blocks for 24–30 students.

vinyl BaSe Ten maT

■■ Durable, 17" x 12" student mat has picture, word, and number columnheadings. Provides reusable work area for regrouping activities.

one-cenTimeTer Graph paper

■■ Perfect for recording Base Ten and Cuisenaire Rod patterns, area,measurement, place value, graphing, and symmetry puzzles.8½" x 11" pads, 100 sheets.

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Base Ten BlocksBase Ten Blocks can be used to— model place value through 9,999 explore addition...

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