# Selected Web Lessons

Many lessons have both a web-based version and a downloadable PDF version.

Click on the lesson title to navigate to the web-based version.

### No. 0001: Build & Explore

- Become familiar with the properties of Digi-Block
- Learn how to pack a block-of-10

1. Build & Explore_0.pdf 102.9 KB

1. Build Explore ws1-3.pdf 73.0 KB

### No. 0003: Building Towers

- Count out a specific number of blocks.

Building Towers.pdf 1486.6 KB

### No. 0009: Bar Graphs

- Use classroom data to make simple bar graphs

9. Bar Graphs.pdf 95.8 KB

9. Bar Graphs ws1-2.pdf 68.7 KB

### No. 001: Rules of the Railroad

- Introduce “good” trains (numbers 10-20)

Rules of the Railroad.pdf 222.3 KB

### No. 002: Introducing Full Cars (Tens) and Blocks Leftover (Ones)

- One-to-one correspondence
- Count by ones to teens
- Introduce place value
- Write the number

002 Introducing Full Cars (Tens) and Blocks Leftover (Ones).pdf 636 KB

### No. 003: Make a Match! (Trains and Numbers)

- Count by ones to 20
- Match quantities with numbers
- Place value

003 Make a Match! (Trains and Numbers).pdf 180 KB

### No. 004: Complete the Trains

- Make a train of a given number

Complete the Trains.pdf 248.3 KB

### No. 005: All Aboard!

- One-to-one correspondence
- Count by ones to teens
- Place value
- Write the number

005 All Aboard!.pdf 732 KB

### No. 012: A Cup of Blocks

- Count to numbers in the 30s
- Write the number

012 A Cup of Blocks.pdf 116 KB

### No. 014: Classify and Count Patterned Shapes

- Recognize geometric basic shapes
- Sort objects within a group by two attributes
- Place blocks with one-to-one correspondence
- Count blocks

Classify and Count Patterned Shapes.pdf 353.1 KB

### No. 016: Train of Tens (36)

- Count by ones
- Begin counting by 10s to 30

016 Train of Tens (36).pdf 112 KB

### No. 017: Keep on Counting – Train of Tens

- Count by tens and ones

017 Keep on Counting – Train of Tens.pdf 116 KB

### No. 018: Connect the Dots (into the 30′s)

- Order written numbers to the 30s

Connect the Dots (into the 30s).pdf 239.5 KB

### No. 019: Ways to make Ten

- Addition Facts
- Match Number Pairs Whose Sum is Ten
- Write Addition Number Sentences

Ways to Make Ten.pdf 149.0 KB

Additional Activities for Ways to Make Ten.pdf 117.1 KB

### No. 020: Cover the Cactus

- Estimate and count the blocks needed to fill a shape

Cover the Cactus.pdf 154.5 KB

### No. 021: One More One Less – How Many Passengers are on the Train

- Determine a number by counting blocks on the train
- Give the number one before and one after

One More One Less – How Many Passengers are on the Train.pdf 239.0 KB

### No. 022: Counting Trains

- Count by tens and ones to the 40s
- Write the number

022 Counting Trains.pdf 208 KB

### No. 023: Ten Scoop

- Addition facts
- Identify number pairs whose sum is 10

023 Ten Scoop.pdf 156 KB

### No. 025: Short and Long Trains

- Recognize numbers to the 50s
- Order numbers from least to greatest
- Write the number

025 Short and Long Trains.pdf 316 KB

### No. 026: Growing Cups

- Estimation using a reference (3-Dimensional)
- Counting

Growing Cups.pdf 144.5 KB

Additional Activities for Estimation.pdf 94.0 KB

### No. 027: Packing Up the Train – Making Blocks-of-10

- Introduce ten ones as one ten
- Introduce the vocabulary: block-of-10
- Identify the place value of the digits

027 Packing Up the Train – Making Blocks-of-10.pdf 164 KB

### No. 028: Introduction to the 2-Place Mat

- Introduce the two-place mat
- Identify the place value of the digits

028 Introduction to the 2-Place Mat.pdf 124 KB

### No. 029: Understanding Two Representations of a Number – Linear and Base Ten

- Introduce different representations of a number
- Identify the place value of the digits

029 Understanding Two Representations of a Number – Linear and Base Ten.pdf 148 KB

### No. 031: Cup to Number Line to Packed

- Count by ones to 30
- Predict the base ten representation of a number
- Compare multiple representations of a number

031 Cup to Number Line to Packed.pdf 148 KB

### No. 032: Combine Two Trains

- Combine two quantities
- Add two two-digit numbers using trains

Combine Two Trains.pdf 362.4 KB

### No. 034: Twelve Ways to Get to Eleven

- Use a number line to determine a quantity
- Recognize that different pairs of addends can combine to make the same sum
- Review the components of a number sentence

Twelve Ways to Get to Eleven.pdf 295.0 KB

### No. 035: What’s Underneath the Covers?

- Recognize the base ten representation of a number
- Reinforce two representations of a number: linear and base ten
- Identify the place value of the digits

035 Whats Underneath the Covers.pdf 260 KB

### No. 036: Pattern of the Count

- Reinforce one-to-one correspondence
- See, hear and write the pattern of the count
- Recognize the base ten number code of digits 0-9
- Identify the place value of the digits

036 Pattern of the Count.pdf 168 KB

### No. 039: Ordering Trains

- Compare and order sets using ordinal numbers
- Build a train to match a drawing
- Count by tens and ones to 30
- Write the number

039 Ordering Trains.pdf 300 KB

### No. 040: How Many is a Cupful?

- Count by ones or tens to the number 50
- Identify the place value of the digits
- Write the number

040 How Many is a Cupful.pdf 124 KB

### No. 043: Two Ways to Look at a Quantity

- Model multiple representations of a number
- Reinforce linear and base ten representations

043 Two Ways to Look at a Quantity.pdf 536 KB

### No. 044: Comparing Trains with Inequality Signs

- Make a set for a given number
- Compare sets using inequality terms and symbols
- Compare attributes of lenth

044 Comparing Trains with Inequality Signs.pdf 236 KB

### No. 050: Adding with Trains

- Model and solve addition problems
- Model regrouping ten ones to make a ten
- Write addition number sentences

050 Adding with Trains.pdf 216 KB

### No. 051: Subtracting with Trains

- Model and solve subtraction problems
- Model regrouping ten ones to make a ten
- Write subtraction number sentences

051 Subtracting with Trains.pdf 292 KB

### No. 057: How Many Packed Blocks

- Write the number for a set of packed blocks

How Many Packed Blocks.pdf 227.5 KB

### No. 058: How Many Boots

- Count to 100
- Recognize three representations of the number 100

How Many Boots.pdf 390.8 KB

### No. 060: A Very Long Train – Counting by 10′s to Numbers Greater than 100!

- Counting by 10′s to numbers greater than 100
- Packing to compare the train or linear view of a number to the base ten view

A Very Long Train.pdf 315 KB

### No. 065: Number Line to Packed Blocks

- Draw packed blocks to represent blocks on a number line

Number Line to Packed Blocks.pdf 270.5 KB

### No. 067: Let’s Get Organized! The 3-Place Mat

- Sort blocks by size
- Organize groups of blocks from largest to smallest
- Set digit cards
- Read 3-digit numbers

Lets Get Organized! The 3-Place Mat.pdf 199.0 KB

### No. 103: Flash!

- Use visual and spatial skills to recognize quantities of blocks
- Make connections between a collection of single blocks and an equivalent representation made up of a block-of-10 and some single blocks
- Represent a number between 10 and 20 with one block-of-10 and some single blocks
- Identify visual patterns that help them “see”

103 Flash!.pdf 61.6 KB

103 Flash Activity Sheet.pdf 10.2 KB

### No. 104: Build a Bigger Block

- Use observation skills and pattern recognition to identify features and similarities among the blocks and the way they pack to form bigger blocks
- Use one-to-one correspondence to count blocks
- Learn that exactly ten blocks are needed to form a bigger block

104 Build a Bigger Block.pdf 57.2 KB

104 Building Blocks Activity Sheet.pdf 46.1 KB

### No. 105: How Much In a Cup

- Use sorting and organizational skills to group blocks into tens and ones to find the total number
- Use reasoning and proof skills as they compare numbers
- Learn to pack as much as possible and sort blocks into tens and ones by placing bigger blocks (the blocks-of-10) to the left of smaller blocks (the singles)

105 How Much In a Cup.pdf 66.5 KB

105 How Much in a Cup Activity Sheet.pdf 8.6 KB

### No. 110: Count by Tens

- Find patterns in the digits as they add and count by tens
- Learn to count by tens from single-digit numbers

110 Count by Tens_0.pdf 69.6 KB

### No. 111: Pack 10

- Students discover and describe patterns. They use spatial reasoning to “see” the blocks present and the blocks missing without necessarily counting. They make connections between number pairs that equal 10 and number pairs that equal 100.
- Students learn to recognize pairs of single-digit numbers with a sum of 10. They also find pairs of multiples of ten that add up to 100, e.g., 20 and 80.

111 Pack 10.pdf 61.3 KB

### No. 112: Together in a Line

- Students connect the physical representation of the addition operation with the equation form. They also connect the meaning of different forms of written equations. Students predict the outcome of addition operations.
- Students learn to write equations in horizontal form and in vertical form. They master how to use blocks on number lines to solve addition problems.

112 Together in a Line.pdf 78.9 KB

### No. 113: Patterns in Regrouping

- Students discover and describe patterns in regrouping. They begin to predict when regrouping will occur with 2- digit addends.
- Students learn to combine packed blocks to model addition.

113 Patterns in Regrouping.pdf 72.6 KB

### No. 114: Ten and Some Extra

- Students begin to think of addition as packing blocks-of- 10 and finding the extra. They connect the single counting view of a teen number with the base ten, packed view of a teen number.
- Students learn to model addition by combining sets of single blocks.

114 Ten and Some Extra.pdf 75.8 KB

### No. 115: Hearts

- To quantify objects on a page
- To compare two quantities
- To find the difference between two quantities
- To enhance spatial awareness
- To analyze what is being asked when presented with a problem
- To develop a strategy to solve the problem
- To extend previous knowledge/experience to a new situation

115 Hearts.pdf 71.5 KB

### No. 116: The Meaning of the Equal Sign

- Students begin to think of the equal sign as a symbol indicating that the quantities on both sides of the equation must balance. This understanding serves as a foundation for early algebraic thinking.
- Students learn to find missing addends.

116 The Meaning of the Equal Sign.pdf 70.1 KB

### No. 117: Making Digi-Block Patterns

- Students make connections between the place value view of a number and the counting view of a number.
- Students learn to describe and make repeating patterns. They learn to organize the blocks by: packing as possible, sorting by size, ordering left to right, and setting the digit cards.

117 Making Digi Patterns.pdf 85.9 KB

### No. 118: Favorite Flavors

- Students invent questions appropriate for a data set. They use problem-solving skills to interpret and solve word problems about the data.
- Students learn to collect and organize data. They learn to solve compare and combine problems.

118 Favorite Flavors.pdf 103.3 KB

### No. 119: Adding on the Mat

- Students predict when to pack a new block-of-10 or “regroup.” Students begin to record what they do with the blocks.
- Students learn to use blocks to model 2-digit addition with and without regrouping.

119 Adding on the Mat.pdf 91 KB

### No. 120: It All Adds Up!

- Students predict sums of 2-digit and 3-digit numbers with and without regrouping.
- Students learn to model addition with blocks and to pack as much as possible to find the sum.

120 It All Adds Up!.pdf 82.4 KB

### No. 121: Thinking About Thirty

- Students describe patterns in the addends that total a given number, in this case 30. They reflect on and describe why the sum is always the same. They relate the number line model to the base ten model as they combine addends.
- Students learn to model complements of 30 using blocks on a number line.

121 Thinking About Thirty.pdf 114.2 KB

### No. 123: Countdown from 100

- Students make connections between packed blocks, number words, and digits.
- Students learn when to unpack a block-of-10 to make more ones available.

123 Countdown from 100.pdf 73.3 KB

123 Countdown from 100 Activity Sheet.pdf 32.3 KB

### No. 124: Separating on the Mat

- Students predict when to unpack a block-of-10 to get some more ones.
- Students learn to use blocks to model 2-digit subtraction with and without regrouping.

124 Separating on the Mat.pdf 79.2 KB

### No. 125: The Cheerios Counting Book

- Students develop basic notions of counting. After students have counted single blocks, they see that they can count the blocks-of-10 as single entities. Students connect the words for counting to 10 to the words for counting by multiples of ten.
- Students learn to count by ones as they pack a block-of- 10. They learn to count from 10 to 20 as they pack a second block-of-10. They also learn to count by tens while they pack a block-of-100.

125 The Cheerios Counting Book.pdf 58.8 KB

### No. 126: Modeling Word Problems

- Students make connections between the blocks and the objects they represent in the story situations.
- Students learn to use the blocks to model situations presented in a variety of word problems. They connect the blocks to the numbers used in the problems.

126 Modeling Word Problems.pdf 67.5 KB

### No. 203: Four Tower Totals

- Observe and reason comparison a number of single blocks with its equivalent representation in packed blocks
- Estimate approximate totals and compare quantities (more and less)
- Combine small sets of single blocks by counting them all and by packing to form collections of tens and ones
- Predict who has more/less and compare sets of blocks

203 Four Tower Totals.pdf 41.3 KB

203 Four Tower Totals Activity Sheet.pdf 25.8 KB

### No. 204: Outside Inside

- Observe, compare, contrast, record, and articulate the features of various sized blocks
- Identify the packing pattern and use this pattern to imagine what is inside each size block

204 Outside Inside.pdf 47.3 KB

204 Outside Inside Activity Sheet.pdf 32.7 KB

### No. 205: Before and After

- Predict what the packed number will look like and name the final number
- Pack single blocks, blocks-of-10, and blocks-of-100 to determine a total amount

205 Before and After.pdf 62.9 KB

205 Before and After Activity Sheet.pdf 29.8 KB

### No. 206: Give and Take

- Use the base ten model for quickly and efficiently adding/removing ten, rather than counting on or back ten
- Name 2-digit numbers by observing blocks-of-10 and ones on a Place Mat
- Add/remove one or ten and note how the number changes

206 Give and Take.pdf 57.3 KB

206 Give and Take Score Sheet.pdf 25.3 KB

### No. 207: Rainbow Number Lines

- Count and name blocks on a number line
- Connect the counting and base ten views of number
- Learn how to use hash marks to facilitate counting and locating numbers on a number line
- Explore ordinal numbers (e.g., ninth, sixteenth, etc.) to identify blocks

207 Rainbow Number Lines.pdf 65.5 KB

207 Rainbow Number Lines Activity Sheet.pdf 36.7 KB

### No. 208: What a Handful Part I

- Organize, interpret and translate physical data to a paper/pencil representation
- Devise and describe estimation strategies
- Construct a physical graph
- Express observations in words and/or numbers
- Name quantities between 10 and 20 by “seeing” tens and ones

208 What a Handful Part I.pdf 72.2 KB

208 What a Handful Part I Activity Sheet.pdf 22.5 KB

### No. 209: What a Handful Part II

- Devise and describe estimation strategies
- Discover features of the Counter and how it works as blocks are loaded
- Observe and describe patterns on the Counter to help them make predictions
- Explore our number system as they use the Counter to predict, load, pack, and name sums up to 3-digit numbers

209 What A Handful Part II.pdf 62.8 KB

209 What A Handful Part II Activity Sheet.pdf 37.2 KB

### No. 212: Two Ways to Take Away

- Students reflect on the process of subtraction as they model problems in two different ways. They explore the connection between the two views of number (counting and place value).
- Students learn to subtract blocks from numbers < 50. Students compare models for subtraction and determine that they will result in the same answer.

212 Two Ways to Take Away.pdf 121.8 KB

218 Spinner for Two Ways to Take Away.pdf 28.1 KB

### No. 213: Regrouping in Addition

- Students discover and describe patterns in regrouping. They predict when and how to regroup.
- Students learn to combine packed blocks to add. They learn to distinguish addition problems that require regrouping from those that do not.

213 Regrouping in Addition.pdf 125.5 KB

### No. 214: Pick a Problem

- Students develop strategies to solve comparison subtraction problems.
- Students learn to model subtraction situations and represent their thinking with blocks, pictures, words, and numbers.

214 Pick a Problem.pdf 101.5 KB

### No. 215: Predict-It Four Square

- Students use mental math and apply their understanding of place value to predict sums of two 2-digit numbers.
- Students learn to predict exact sums of two 2-digit addends. Students verify answers with blocks.

215 Predict-It Four Square.pdf 93 KB

### No. 216: Predict and Check

- Students develop strategies for predicting sums and differences of 2-digit numbers.
- Students learn to make accurate predictions and to check predictions with blocks and algorithms.

216 Predict and Check.pdf 77 KB

### No. 218: From Blocks to Drawings to Numbers

- Students model a problem with blocks then transfer the model to a drawing. They represent the process with numbers by writing number sentences (showing partial sums) as they move towards developing an algorithm.
- Students learn how to record an addition problem with drawings of blocks and numbers.

218 From Blocks to Drawings to Numbers.pdf 108 KB

### No. 219: Holders and Blocks

- Students draw equal groups and record the multiplication number sentence. They share strategies used to determine the product and compare products to name the winner of each game round.
- Students learn to express equal groups as a multiplication number sentence. They identify the meaning of each factor in the number sentence and accurately name the product.

219 Holders and Blocks.pdf 106 KB

### No. 220: Recording Subtraction

- Students make connections between the blocks and the symbolic representation.
- Students model a problem with blocks and represent with a drawing what they do with the blocks.

220 Recording Subtraction.pdf 110 KB

### No. 224: Problem Patterns

- Students describe the relationship of problems in a set and use reasoning to determine sums. They discover properties of addition and develop mental math strategies.
- Students learn to predict sums by using patterns identified in related problems. They check predictions with blocks.

224 Problem Patterns_0.pdf 55 KB

224 Problem Patterns Activity Sheet.pdf 30 KB

### No. 225: 100 Hungry Ants

- Students explore different representations of 100. They find many factors of 100, and practice counting by those multiples to 100. Students apply what they learn to different numbers.
- Students learn to count to 100 by 1s, 50s, 25s, 20s and 10s.

225 100 Hungry Ants.pdf 73 KB

### No. 228: Problem Pairs

228 Problem Pairs.pdf 71 KB

### No. 303: Making Castles

- Use pattern and observation skills to recognize and create equivalent representations of a number
- Use group cooperation skills, spatial reasoning skills and group organizational skills to build a castle
- Recognize equivalent representations of a number given in various collections of blocks

303 Making Castles_0.pdf 58.5 KB

303 Making Castles Activity Sheet.pdf 37.1 KB

### No. 304: Do You See What I See

- Students use observation skills to compare, contrast, and name different features of the blocks. They also use spatial skills as they build structures with the blocks. Students use communication skills to give and follow directions accurately.
- Students learn to name and describe the different-sized blocks and provide criteria for distinguishing amongst the blocks.

304 Do You See What I See.pdf 58.3 KB

304 Do You See What I See Activity Sheet.pdf 37.1 KB

### No. 306: The Great Penny Push

- Students use estimation skills and spatial skills to conduct the penny push.
- Students learn to represent numbers in two ways: as a long string of single blocks along a number line and also in the base ten view. They make connections between these two views of numbers.

306 The Great Penny Push.pdf 53.0 KB

306 The Great Penny Push Activity Sheet.pdf 28.0 KB

### No. 307: The Big Count

- Students model the sequence of 3-place numbers. They identify and describe the repeating patterns of digits in the number code. Students use number sense to estimate and then to verify where 3-place numbers are located on a number line. Students relate the base ten view of number to the number line view.
- Students use blocks on the Counter to model, name, and write numbers from 0 to 1000. They practice counting by tens and hundreds.

307 The Big Count.pdf 66.8 KB

307 The Big Count Activity Sheet.pdf 22.0 KB

### No. 308: Numbers Incognito

- Students explore different ways to model 3-place numbers, and identify patterns in these representations.
- Students learn to recognize multiple representations of a number. This skill greatly enhances their ability to “regroup” when performing operations.

308 Numbers Incognito.pdf 55.4 KB

### No. 309: Give and Take From 200

- Students “see” the value of the base ten model and number code for quickly adding/removing one, ten or one hundred from a number.
- Students model and name 3-digit numbers. Students develop mental math strategies as they predict, then check their predictions with blocks. Students compare numbers and name differences of one, ten, or one hundred.

309 Give and Take From 200.pdf 63.4 KB

309 Give and Take From 200 Score Sheet.pdf 24.6 KB

### No. 310: Closer To

- Students use number sense to create a number closest to a given number. They use reasoning and mathematical ideas to compare numbers and determine which of two is closer to 0, 250, 500, or 1000.
- Students develop strategies (counting up, using a number line, blocks, or algorithm) for naming exact differences between numbers.

310 Closer To.pdf 102.0 KB

### No. 311: Measuring the Blocks

- Students make predictions and draw conclusions from information obtained. Students critique their process and results.
- Students measure length, width, and height of different sized blocks. Using this information, they estimate the size of the block-of-1000. They compare estimates to discuss reasonableness of answers.

311 Measuring the Blocks.pdf 89.9 KB

### No. 312: Whats Your Story

- Students apply the concept of repeated addition to beginning ideas about multiplication. They make connections between the models of equal groups and the corresponding multiplication sentences and stories.
- Students use blocks to model repeated addition and equal groups. They learn to write multiplication sentences represented by the blocks and to write stories to go with these sentences.

312 Whats Your Story.pdf 456.4 KB

### No. 313: Predict in a Row

- Students use number sense, estimation, and mental math skills to predict the two addends that make a given sum.
- Students learn to determine exact sums of two numbers. Students check their work by modeling problems with the blocks.

313 Predict in a Row.pdf 98.9 KB

313 Worksheets.pdf 58.8 KB

### No. 314: Seeing Addition in Two Ways

- Students reflect on the process of addition as they solve problems using two different models. They explore the connection between the two views of number (counting and place value) as they represent addends and sums on the number line and with packed blocks.
- Students learn to combine addends to make sums < 400. Students compare models for addition and determine that they will result in the same sum.

314 Seeing Addition in Two Ways.pdf 187.8 KB

### No. 315: Race To Zero

- Students recognize when regrouping is necessary as they model subtraction problems.
- Students learn to model and record subtraction with and without regrouping.

315 Race To Zero.pdf 56.2 KB

### No. 316: Let’s Explore 6 x 4

- Students select materials to illustrate multiplication problem situations. They reflect on different models and conclude that they get the same solution regardless of the model chosen.
- Students learn to model, record, and solve 1-digit x 1- digit multiplication problems.

316 Let’s Explore 6 x 4.pdf 115.5 KB

### No. 317: Flossing Facts

317 Flossing Facts.pdf 125.9 KB

### No. 320: Cover Up

- Students model “growing” products as they use blocks to compare facts such as 3 x 4, 3 x 40, and 3 x 400. They note the shift to the left in the products, from 12, to 120, and 1200. Students explore commutativity and verify that the order of the factors (10 x 4, 4 x 10) does not affect the product.
- Students learn to multiply tens and hundreds by a single digit number.

320 Cover Up.pdf 131.0 KB

### No. 321: Building Multiplication Tables

- Students use skip counting and known facts to find products.
- Students learn to model single digit multiplication in an array.

321 Building Multiplication Tables.pdf 121.0 KB

### No. 323: Fish Stories

- Students use packed blocks to model the base ten representation of multiplication of a 2- or 3-digit number by 3. They begin to develop an algorithm as they “show what they do with numbers.”
- Students learn to model, record, and express 2-digit by 1-digit multiplication with numbers.

323 Fish Stories.pdf 176.7 KB

### No. 324: Problem Patterns

- Students describe the relationship of problems in a set and use reasoning to determine sums. They discover properties of addition and develop mental math strategies.
- Students learn to predict sums by using patterns identified in related problems. They check predictions with blocks.

324 Problem Patterns.pdf 63.6 KB

324 Worksheets.pdf 56.8 KB

### No. 325: Ten Times Better

- Students model each animal’s number and relate the block model to the book’s illustration. Students predict each successive animal’s number and its representation with blocks.
- Students learn to multiply single-digit numbers by ten.

325 Ten Times Better.pdf 85.6 KB

### No. 326: Even Shares

- Students use their intuitive sense of sharing materials evenly to conduct even share activities.
- Students learn to use the blocks to represent a division problem. They connect the blocks to the numbers used in the problem.

326 Even Shares.pdf 100.0 KB

### No. 327: Reverse and Compare

- Students reverse the order of the factors in multiplication problems in order to compare the two models. They discover that changing the order of the factors does not matter when modeling multiplication. Yet, changing the order can make the multiplication easier.
- Students learn to reverse the order of the factors if the computation is more efficient.

327.3 Reverse and Compare.pdf 57.5 KB

### No. 328: Sharing vs. Equal Groups

- Students explore two meanings for division by modeling different situations with blocks. They first examine a problem and decide which model or meaning of division is most appropriate and then use that model to solve the problem.
- Students learn to model, solve, and write number sentences to represent division story problems.

328.2 Sharing vs. Equal Groups.pdf 88.0 KB

328 Worksheets.pdf 60.2 KB

### No. 403: Race to 500

- Students use pattern recognition and reasoning to discover that because our number system only has 10 digits, they must group their blocks in tens if they want to express the total number.
- Students build and recognize numbers represented in hundreds, tens, and ones. Students learn the pattern of grouping by tens inherent in our number system. They learn to pack groups of 10 blocks into holders and move them to the correct place value position.

403 Race to 500.pdf 55.3 KB

### No. 404: Pack, Pack, Pack

- Students develop strategies to determine when regrouping is necessary and then articulate a rule.
- Students will pack a collection of single blocks until they cannot do any more packing and will identify the digits that represent the collection of blocks.

404 Pack, Pack, Pack_0.pdf 48.4 KB

404 Pack, Pack, Pack Activity Sheet.pdf 27.7 KB

### No. 405: Mark the Spot

- Students use logical reasoning to make connections between two views of the same number.
- Students link a location on a number line with a specific collection of packed blocks.

405 Mark the Spot_0.pdf 39.4 KB

### No. 406: Measurement Scavenger Hunt

- Students use logical reasoning to make connections between two views of the same number.
- Students link a location on a number line with a specific collection of packed blocks.

406 Measurement Scavenger Hunt_0.pdf 53.7 KB

406 Measurement Scavenger Hunt Activity Sheet.pdf 42.0 KB

### No. 407: Go and Stop

- Students use classification skills to sort the blocks by size according to place value. They make connections between the different representations of a number.
- Students learn to create and record equivalent representations of a number.

407 Go and Stop_0.pdf 51.8 KB

407 Go and Stop Activity Sheet.pdf 28.2 KB

### No. 410: How Big Is It

- Students problem solve in order to obtain necessary information. They draw conclusions from information obtained. They critique their process and results.
- Students measure length and width and depth of a block of 100. Using this information, they estimate the size of the block-of-10,000. They compare estimates to discuss reasonableness of answers.

410 How Big Is It_0.pdf 57.6 KB

410 How Big Is It Activity Sheet.pdf 24.7 KB

### No. 411: Digit Shuffle

- Students use number sense to create a 3-digit number that fits a description. They compare the number to another number and explain their reasoning as they decide which fits the description better.
- Students learn to compare larger blocks or values first, as they order 3-digit numbers. They learn characteristics of even and odd numbers and practice comparing numbers according to size or location closer to a number between 1 and 1000.

411 Digit Shuffle.pdf 139.1 KB

411_worksheets_for_Digit_Shuffle.pdf 95.7 KB

### No. 412: The Greatest Difference

- Students use strategies to create equations. They look for patterns in the number of possible equations. The also compare and contrast different methods for solving subtraction problems with blocks.
- Students use single blocks on the number line to subtract. They learn to use packed blocks on the Place mat to subtract. They learn that both methods produce the same mathematical result.

412 The Greatest Difference.pdf 111.4 KB

412 Worksheets.pdf 61.8 KB

### No. 413: It’s a Match

- Students relate knowledge of “basic facts” to multiplication with large numbers.
- Students learn to multiply large numbers by using blocks of corresponding size to represent similar multiplication problems (i.e. 5 X 3, 5 X 30, 5 X 300).

413 It’s a Match.pdf 105.1 KB

413 Worksheet.pdf 5.7 KB

### No. 414: The Any Way Array

- Students relate their understanding of repeated addition and of basic multiplication facts to multiplication with numbers 11-25.
- Students learn to model arrays with 2-digit numbers and to write corresponding multiplication sentences. They learn to find the total number of blocks (the product) for a given array.

414 The Any Way Array.pdf 131.5 KB

414 Worksheets.pdf 61.1 KB

### No. 415: The Digi-Block Shift

- Students look for and identify patterns in the way the digits and the blocks shift when a number is multiplied by ten. They use this pattern to predict a product.
- Students learn what it means to “shift the digits” as a visual representation for multiplying by ten.

415 The Digi Shift.pdf 99.9 KB

415 Worksheet.pdf 14.3 KB

### No. 416: It’s a Snap

- Students connect their understanding of basic multiplication facts to models of 2-digit X 1-digit multiplication.
- Students learn to use blocks to model 2-digit X 1-digit multiplication.

416 Its a Snap.pdf 107.6 KB

416 Worksheet.pdf 5.1 KB

### No. 417: Predict Before You Pack

- Students use their base ten understanding to predict products.
- Students learn to set digit cards to predict products and then to check their predictions by packing the blocks.

417 Predict Before You Pack.pdf 90.9 KB

417 Worksheet.pdf 9.7 KB

### No. 418: In The Middle

- Students apply their understanding of multiplication to predicting one of the factors.
- Students learn to relate one factor and the product in a multiplication sentence in order to determine the other factor.

418 In The Middle.pdf 92.7 KB

418 Worksheet.pdf 7.3 KB

### No. 419: Leave a Trail

- Students use the Digi-Block materials to relate their understanding of multiplication to paper-and-pencil recording techniques.
- Students learn to record, in their own manner, how they use the blocks to solve a multiplication story problem.

419 Leave a Trail.pdf 137.1 KB

419 Worksheets.pdf 63.4 KB

### No. 420: Enough Stuff

- Students use their understanding of multiples of ten to predict products.
- Students learn to represent and solve multiplication story problems with blocks.

420 Enough Stuff_0.pdf 116.4 KB

### No. 423: Let’s Share

- Students use their intuitive sense of sharing materials fairly to conduct fair share activities.
- Students learn to use the blocks to represent a division problem. They connect the blocks to the numbers used in the problem.

423 Let’s Share.pdf 97.1 KB

423 Worksheet.pdf 4.0 KB

### No. 424: Three Ways to See 48 divided by 3

- Students select materials to illustrate problems that can be modeled with division. They examine different models and conclude that the solution is the same regardless of the model.
- Students learn to model, record, and solve 2-digit divided by 1- digit problems.

424 Three Ways to See 48 Div By 3.pdf 135.0 KB

424 Worksheets.pdf 50.2 KB

### No. 425: The Incredible Comparisons

- Students use their conceptual understanding of addition, subtraction, multiplication, and division to pose questions and make comparisons presented in the book. They also make connections between mathematics and real-world situations.
- Students learn to pose, model, and solve comparison situations. They learn to illustrate their solution and to write appropriate mathematical equations.

425 The Incredible Comparisons.pdf 124.3 KB

### No. 426: Two Ways to Divide

- Students explore two meanings for division by modeling different situations with blocks. They examine the relationship between the two models and decide which model best reflects a division situation as they solve it with blocks.
- Students learn to model, solve, and write number sentences that match division story problems.

426 Two Ways to Divide.pdf 129.0 KB

### No. 513: Tenths and Hundredths

- Represent decimal numbers using blocks on place value mats
- Read and write decimal numbers
- Observe, describe and extend patterns

1.3 Tenths and Hundredths.pdf 568 KB

### No. 515: Compare Numbers

- Identify the greater of two decimal numbers
- Use the greater than (>) and less than (<) symbols to indicate relationships between numbers
- Put a list of decimal numbers in order from least to greatest

1.5 Compare Numbers.pdf 520 KB

### No. 522: Use Blocks to Add

- Understand the basic meaning of addition as joining sets
- Use a physical and visual model to add whole numbers and decimal numbers
- Describe with words and pictures what happens in each place when numbers are added
- Understand regrouping in addition

2.2 Use Blocks to Add.pdf 540 KB

### No. 532: Extend the Facts

- Use place value to extend students’ knowledge of basic facts to multiply larger numbers
- Observe, describe and extend patterns.

3.2 Extend the Facts.pdf 488 KB

### No. 533: Find Partial Products

- Recognize the validity of the distributive property through the use of physical models
- Identify the partial products according to each place in a 1-digit by 2-digit multiplication problem
- Express a multiplication problem as the sum of two or more partial products

3.3 Find Partial Products.pdf 512 KB

### No. 541: Multiply with Tenths and Hundredths

- Multiply using the block models for tenths and hundredths
- Understand the concept of multiplying by a number less that 1
- Use the commutative property to solve problems in the easiest way

5.1 Multiply with Tenths and Hundredths.pdf 500 KB

### No. 542: Record Division by Single Digit Numbers

- Connect concrete division with blocks to symbolic division using numbers
- Solve problems with single-digit divisors
- Understand the steps of the traditional division algorithm

4.2 Record Division by Single Digit Numbers.pdf 540 KB

### No. 543: Divide by Multiples of 10

- Explore ways to divide a number by 10 and by 100
- See that dividing a number by 10 results in a number with the same digits shifted one place to the right
- Extend division facts to solve problems with multiples of 10

4.3 Divide by Multiples of 10.pdf 112 KB

### No. 552: Multiply by 0.01 and by 0.001

- Understand the special properties of multiplying by 0.1 and by 0.01
- Think of multiplying by 0.1 and by 0.01 as replacing each block with a block one or two sizes smaller
- See that multiplying by 0.1 and by 0.01 yields the same result as dividing by 10 and by 100

5.2 Multiply by 0.01 and by 0.001.pdf 508 KB

### No. 562: Divide by 0.1 and by 0.01

- Understand that dividing a number by 0.1 results in a number with the same digits shifted one place larger
- Understand that dividing a number by 0.01 results in a number with the same digits shifted two places larger
- See that dividing by 0.1 and 0.01 yields the same result as multiplying by 10 and by 100

6.2 Divide by 0.1 and by 0.01.pdf 500 KB

### No. 572: Connect Percents, Ratios, Fractions and Decimals

- Understand the percents and the words and symbols for them
- Write any number as a fraction, a decimal or a percent

7.2 Connect Percents, Ratios, Fractions and Decimals.pdf 704 KB

### No. 573: Fractions and Percents of a Set

- Identify factors and fractional parts of a number
- Use 10%, 5% and 1% to quickly identify percents of any number

7.3 Fractions and Percents of a Set.pdf 504 KB

### No. 574: Powers of 10

- Use exponents when describing repeated factors of the same number
- Write powers of 10 using exponential notation, including 10
^{0}=1 - Use powers of 10 and expanded notation to describe multi-digit numbers

7.4 Powers of 10.pdf 500 KB

### No. AB4-9: Packing Coins and Bills

- Associate number name, number symbol and place value meaning for dimes and pennies
- Given a collection of $1 bills, dimes and pennies, determine the correct value

Unit 4, Lesson 9.pdf 103 KB

### No. EM 2 11.3: 100 Hungry Ants

- Represent 100 in multiple ways

EM 2 11.3 100 Hungry Ants.pdf 120 KB

### No. EM 2 11.4: Equal Sharing and Equal Grouping

- Solve division problems through modeling with the blocks

EM 2 11.4 Equal Sharing and Equal Grouping.pdf 116 KB

### No. EM 2 11.6: Products Table

- Build a product table to learn and understand multiplication facts

EM 2 11.6 Products Table.pdf 160 KB

### No. EM 2 11B: Multiply to Divide

- To model and explain division as the inverse of multiplication
- To write number sentences to show the division/multiplication relationship of three given numbers

EM 2 11B Multiply to Divide.pdf 130.9 KB

### No. EM 2 1A: The Pattern of Packing

- To discover relationships among the single blocks, blocks-of-10, blocks-of-100 and blocks-of-1000
- To record, observe, compare and articulate the features of blocks of each size, to identify the pattern of the packing, and to use this pattern to imagine what is inside each size block

EM 2 1A The Pattern of Packing.pdf 272 KB

### No. EM 2 1B: Pattern of the Count

- To use the blocks to model, write and read the numbers from 0 to 1000 in sequence
- To identify patterns in the numbers from 0 to 1000 and to describe why they occur and how they relate to what is happening with the blocks

EM 2 1B Pattern of the Count.pdf 148 KB

### No. EM 3 9.11: Partial Products Two-Digit Numbers.pdf

EM 3 9.11 Partial Products Two-Digit Numbers.pdf 156KB

### No. EM 3 9.3: Arrays to Model Partial Products

EM 3 9.3 Arrays to Model Parial Products.pdf 176KB

### No. EM 3 9.3: Arrays to Model Partial Products

EM 3 9.3 Arrays to Model Parial Products.pdf 176KB

### No. EM 3 9.4: Partial Products

EM 3 9.4 Partial Products.pdf 152KB