Grade 4
Grade 4
Mathematics
Table of Contents
Unit 1: Understanding Multi-Digit Whole Numbers 1-1
Unit 2: Performing Multi-Digit Whole Number Addition and Multiplication 2-1
Unit 3: Performing Multi-Digit Whole Number Subtraction and Division 3-1
Unit 4: Solving Algebra and Pattern Problems 4-1
Unit 5: Measurement 5-1
Unit 6: Fractions and Decimals 6-1
Unit 7: Geometry 7-1
Unit 8: Building Mathematical Fluency 8-1
2012 Louisiana Transitional Comprehensive Curriculum
Course Introduction
The Louisiana Department of Education issued the first version of the Comprehensive Curriculum in 2005. The 2012 Louisiana Transitional Comprehensive Curriculum is aligned with Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS) as outlined in the 2012-13 and 2013-14 Curriculum and Assessment Summaries posted at . The Louisiana Transitional Comprehensive Curriculum is designed to assist with the transition from using GLEs to full implementation of the CCSS beginning the school year 2014-15.
Organizational Structure
The curriculum is organized into coherent, time-bound units with sample activities and classroom assessments to guide teaching and learning. Unless otherwise indicated, activities in the curriculum are to be taught in 2012-13 and continued through 2013-14. Activities labeled as 2013-14 align with new CCSS content that are to be implemented in 2013-14 and may be skipped in 2012-13 without interrupting the flow or sequence of the activities within a unit. New CCSS to be implemented in 2014-15 are not included in activities in this document.
Implementation of Activities in the Classroom
Incorporation of activities into lesson plans is critical to the successful implementation of the Louisiana Transitional Comprehensive Curriculum. Lesson plans should be designed to introduce students to one or more of the activities, to provide background information and follow-up, and to prepare students for success in mastering the CCSS associated with the activities. Lesson plans should address individual needs of students and should include processes for re-teaching concepts or skills for students who need additional instruction. Appropriate accommodations must be made for students with disabilities.
Features
Content Area Literacy Strategies are an integral part of approximately one-third of the activities. Strategy names are italicized. The link (view literacy strategy descriptions) opens a document containing detailed descriptions and examples of the literacy strategies. This document can also be accessed directly at .
Underlined standard numbers on the title line of an activity indicate that the content of the standards is a focus in the activity. Other standards listed are included, but not the primary content emphasis.
A Materials List is provided for each activity and Blackline Masters (BLMs) are provided to assist in the delivery of activities or to assess student learning. A separate Blackline Master document is provided for the course.
The Access Guide to the Comprehensive Curriculum is an online database of suggested strategies, accommodations, assistive technology, and assessment options that may provide greater access to the curriculum activities. This guide is currently being updated to align with the CCSS. Click on the Access Guide icon found on the first page of each unit or access the guide directly at .
Grade 4
Mathematics
Unit 1: Understanding Multi-Digit Whole Numbers
Time Frame: Approximately four weeks
Unit Description
Mastery of numbers including counting, writing, comparing, rounding, estimating and ordering large numbers (to 1,000,000) using place value strategies is achieved. Connections are made regarding the relationships among place values. Number patterns resulting from operations are examined, the corresponding rules are stated, and predictions are made concerning next terms.
Student Understandings
Students demonstrate an understanding of place value in writing and comparing large numbers to 1,000,000. They utilize number patterns to predict missing elements in a pattern.
Guiding Questions
1. Can students demonstrate an understanding of large numbers to 1,000,000?
2. Can students explain how a digit in one place represents ten times what it represents in the place to its right?
3. Can students read, compare, and order large numbers to 1,000,000 using place value strategies?
4. Can students round to the specific place values?
5. Can students investigate and determine patterns in place value and in odd-even numbers and generalize these patterns?
Unit 1 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 using place value concepts, standard notation, and models |
| |through 1,000,000 (N-1-E) (N-3-E) (A-1-E) |
|10. |Solve multiplication and division number sentences including interpreting remainders (N-4-E) (A-3-E) |
|Patterns, Relations, and Functions |
|43. |Identify missing elements in a number pattern (P-1-E) |
|CCSS for Mathematical Content |
|CCSS # |CCSS Text |
|Operations and Algebraic Thinking |
|4.OA.5 |Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that|
| |were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, |
| |generate terms in the resulting sequence and observe that the terms appear to al-ternate between odd and |
| |even numbers. Explain informally why the numbers will continue to alternate in this way. |
|Number and Operations in Base Ten |
|4.NBT.1 |Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents |
| |in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and|
| |division. |
|4.NBT.2 |Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare |
| |two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record |
| |the results of comparisons. |
|4.NBT.3 |Use place value understanding to round multi-digit whole numbers to any place. |
|ELA CCSS |
|CCSS # |CCSS Text |
|Writing Standards |
|W.4.2d |Write informative/explanatory texts to examine a topic and convey ideas and information clearly. Use precise|
| |language and domain-specific vocabulary to inform about or explain the topic. |
|Speaking and Listening Standards |
|SL.4.1 |Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with |
| |diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. |
| |Follow agreed-upon rules for discussions and carry out assigned roles. |
| |Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on|
| |the remarks of others. |
Sample Activities
Activity 1: Place Value Vocabulary (CCSS: 4.NBT.2, 4.NBT.3)
Materials List: Place Value Vocabulary BLM
Have students create a place value vocabulary self-awareness chart, (view literacy strategy descriptions) for the following terms: place value, value, period, numeral, digit, standard form, expanded form, word form, and rounding. The self-awareness chart will help the students draw upon their prior knowledge and provide a base-line for their knowledge of place value. Provide students the vocabulary self-awareness BLM and have them complete a self assessment of their knowledge of the words. Do not give the students definitions or examples at this stage.
Ask students to rate their understanding of each word before the lesson begins. A plus sign (+) indicates a high degree of comfort and knowledge, a check mark (√) indicates uncertainty, and a minus sign (–) indicates the word is brand new to them. Ask students to try to supply a definition and an example for each term. For words with check marks or minuses, students may have to make guesses about definitions and examples. Give students time throughout the unit to return to their self-awareness chart to revise their entries. Returning to their charts will give them multiple opportunities to practice and extend their understanding of key place value terms.
|Word |+ |√ |– |Example |Definition |
|Place Value | | | | | |
|Value | | | | | |
|Period | | | | | |
Activity 2: Getting to Know a Million (GLE: 2; CCSS: 4.NBT.1, 4.NBT.2, SL.4.1c)
Materials List: base ten blocks or Grid Paper BLM, calculator, ruler
Ask students to discuss what they know about the number one million. They may mention that it has six zeros, it’s an even number or it’s a lot of money. Help students understand the number by using various ways to visualize it. One way is to use the flat that represents 100 from a set of base ten manipulatives. If none are available, the Grid Paper BLM can be used. Ask the following questions:
• What number does one row of ten flats represent? (1000)
• What number does a square consisting of ten rows of ten flats represent? (10,000)
• What number does a row of ten such squares represent? (100,000)
• What number does a square of ten such rows represent? (1,000,000)
To help students understand the repetitive nature of our number system, ask which numbers can be modeled with a cube. (1; 1,000; 1,000,000; etc.) Which numbers can be modeled with a rod or strip? (10; 10,000; 10,000,000; etc.) Which numbers can be modeled with a flat? (100; 100,000; 100,000,000; etc.)
Use illustrations to help students visualize the amounts. Have students draw a square representing one flat and label it as 100. Have them create the pictures using that square to represent the numbers in the questions above. As students go through the example, help them relate to the expanded and written forms of numbers. Use other examples to illustrate the relative size of large numbers. Ask students to predict how long it would take for a hundred seconds to tick away (1 minute and 40 seconds), and a thousand seconds (16 minutes and 40 seconds), and a million seconds (11 days, 13 hours, and 47 minutes). Show the students the answers using a calculator. Another example would be to find the lengths of a hundred inches, a thousand inches, and a million inches.
Activity 3: Number Patterns (GLE: 10; CCSS: 4.NBT.1, 4.NBT.2, W.4.2d)
Materials List calculators for each student, math learning log, pencils
Have students maintain a math learning log (view literacy strategy descriptions). This is a notebook that students can use to record ideas, questions, reactions, and new understandings. Documenting ideas in a log about the content being studied allows students to explain their thinking in words. Writing their thoughts and processes down in a notebook helps students reflect and can lead to further learning.
In this activity, students will look for patterns to help them understand how place values are related. The goal is for students to realize that a digit in one place represents ten times what it represents in the place to its right. Ask students what do I multiply 6 by to get 60? (10) What do I multiply 60 by to get 600? (10) Have students work in groups, but provide each student with a calculator. Have students use the calculator to find the missing factor. Have students record their observation in their math learning log. Have students use their calculators to divide 60 ( 6; 600 ( 60; 6,000 ( 600. Have students write their observations in their math learning log. Discuss the patterns that they see using place value vocabulary. Some sample responses might be that every answer is ten or that each divisor is one place value smaller than the dividend. Repeat the activity using these problems: 600 ( 6; 6,000 ( 60; 60,000 ( 600; 6,000 ( 6; 60,000 ( 60. Again, have students write their observations in their math learning log and discuss any patterns they see. Ask questions such as these: What is the place value of the digit 6 in the divisor and dividend? How are the two numbers related? How are the place values of the digit 6 related in the questions 600 ( 6; 6,000 ( 60, etc.? What conclusions can we draw about how the place values are related? What do I have to multiply the divisor by to get the dividend? Have students discuss how a digit in one place represents ten times what it represents in the place to its right.
Have students answer questions such as these: If I am 8, what do I have to be multiplied by to become 80? If I am 40, what do I have to be multiplied by to become 400? If I am 30, what do I have to be multiplied by to become 3,000? Have students write their observations in their math learning log and discuss how they found their answers.
Consider repeating this activity later in the unit when numbers are compared.
Activity 4: Converting Place Value (GLE: 2; CCSS: 4.NBT.2)
Materials List: base-ten blocks, math learning log, pencils
Have students work in groups and provide each group with base-ten blocks. Have students use the blocks to create 135. The students should start with 1-hundreds block, 3-tens blocks, and 5 ones-blocks. Have students draw a picture of what their blocks look like in their math learning log (view literacy strategy descriptions). Be sure that the students label each part of the picture (1-hundreds, 3-tens, and 5-ones). Discuss with the students how the three parts are combined to make 135. Have students write the number in expanded form using the value of each part.
1 hundreds 3 tens 5 ones
100 + 30 + 5 = 135
Now, tell the students they need to use the blocks to make 135 again but they can no longer use the hundreds block. Observe how the students approach the problem. Did the students replace the hundreds block with 10 tens blocks? Did the students replace all the blocks with 135 ones blocks? Did they ask how they could make 135 without a hundred? When the students finish the problem, have them draw their answer in their math learning log and write how they were able to make 135 without a hundreds block. Discuss as a class how students approached and solved the problem. If the students did not suggest it on their own, demonstrate that 135 can also be 13 tens and 5 ones as well as 135 ones. Have students check their answers by writing the value of each of their block groups and adding the parts to see if it still equals 135. Have students discuss how a digit in one place represents ten times what it represents in the place to its right.
Continue giving students other place value conversion problems in which they begin with the blocks for each place value and then are no longer allowed to use one of the place values. Try numbers in which students are no longer allowed to use tens blocks, numbers that have multiple hundreds, or numbers that have a thousands place.
Activity 5: Find Your Partners (GLEs: 2; CCSS: 4.NBT.2)
Materials List: large 5 ( 7 index cards with numbers written in corresponding standard, word, and expanded form, Find Your Partners BLM
Make a copy of the Find Your Partner BLM. Cut the cards apart and distribute one card to each student. Have each student write the information from his/her card on a large index card. When everyone has finished writing their information on a card, have them quietly move around the room to find their partners. When each group has found their number in written, standard, and expanded forms, have them read their cards aloud. If the class agrees, have them give a thumbs-up. If they disagree, have the class give a thumbs-down. Any group receiving a thumbs-down needs to try again to find the correct partners.
Activity 6: Number Loops (CCSS: 4.NBT.2)
Materials List: paper, pencil, post its
Have the students practice making number loops. This will give them practice with numbers written in standard and word form. Numbers will always loop back to 4.
Begin by writing any number in standard form. Next, write that same number in word form. Next, count the letters in the written form. Write that number in standard form. Continue the pattern of word form, standard form until the number loops to 4.
Sample 1 Sample 2
378,010 6,907
Three hundred seventy-eight thousand ten six thousand nine hundred seven
35 27
thirty-five twenty-seven
10 11
ten eleven
3 6
three six
5 3
five three
4 5
five
4
Give each student a post-it sheet. Have them write a number between 35,001 and 75,009 at the top of the sheet using standard form. Have them write the number they chose in word form and in expanded form. Have the students place their number on a Venn diagram that has one circle labeled---even numbers and the other circle labeled numbers greater than 50,000. Have the class discuss any numbers that they disagree with on the placement. (Don’t forget to discuss the numbers that belong on the outside of the circles and the numbers that would be shared by both circles.)
Even Numbers Numbers > 50,000
[pic]
Activity 7: Rounding Text Chain (GLE: 2; CCSS: 4.NBT.2, 4.NBT.3, SL.4.1b)
Materials List: pencil, paper
Have students work with partners or in groups of four using a modified text chain (view literacy strategy descriptions). Text chains give students the opportunity to demonstrate their understanding of newly learned material. In this modified version, students pass along a problem from one person to another with each student solving part of the problem. This collaborative process allows students to demonstrate their newly learned knowledge and reflect upon it within a group.
Review with students the process of rounding to the nearest place value. Give each group a number to the ten thousands place. Have the first person in the group round the number to the nearest tens place. Have the students pass the number to the next person and have them round the original number to the hundreds place. Continue this process until the original number has been rounded to the ten thousands place. As the students round, have them explain to the group why they rounded the way they did.
Continue this activity with numbers to the millions place, numbers that contain 9’s, or have students create their own numbers to challenge their group members. Observe students’ rounding and their explanations.
Activity 8: Develop a Sense of Large Numbers (GLE: 2; CCSS: NBT.2, NBT.3)
Materials List: clock, calculator, How Much is a Million? by David Schwartz, estimation materials, (e.g., beans on the overhead, rice in a jar, pretzels in a bag, etc.)
Have students count for a given amount of time (one minute for example). Using the number to which they counted as a benchmark, have them round their number to the nearest hundred. Using the rounded number, have the students use a calculator or mental math to predict how long it would take them to count to 1000, to 10,000, to 100,000, to 1,000,000. Read How Much Is a Million? by David M. Schwartz. Have them compare their predictions to the book.
• Give the students many varied opportunities to estimate large quantities of objects throughout this unit using a benchmark (e.g., beans on the overhead, dots that can be drawn in one minute, rice in a jar, pretzels in a bag, etc.). Note: Show students how food items can be estimated by using the amount of an individual serving and the number of servings in a container.
Example:
(Amount in an individual serving) ( (Number of servings) = (Estimated amount of items in the container).
Activity 9: Read, Write, Compare, and Order (GLE: 2; CCSS: 4.NBT.2)
Materials List computer, encyclopedias, or current atlas, math learning log, pencil
Provide student groups with a list of several cities in Louisiana. Have students research (using the computer, encyclopedias, current atlas, etc.) to find the most current population of each city and have them compare the populations and put them in order from smallest to largest. Have them record this information in their math learning log (view literacy strategy descriptions).
Activity 10: Number Grid Puzzles (GLEs: 2, 43; CCSS: 4.OA.5, 4.NBT.2)
Materials List: grid paper taped together to create large number chart for recording numbers, number cards, marker, Number Grid Puzzles BLM
Center activity---Have students study the patterns of numbers by creating a number chart of large numbers (for instance, from 10,000 to 11,000). Place a variety of numbers on the chart in sequential order. The numbers should be chosen so that students can make for simple calculations. Pick numbers that are related; such as 10, 100, 1000; and their multiples and factors. Make number cards (with a specific number on each card) available for a student to choose. Using place value and number pattern strategies have them locate the placement of that number and write the number on the chart.
Example: A student chooses a card. It has 4,787 on it. The student, using place value and number pattern strategies, writes that number in the appropriate space on the number chart. This center activity remains open until all the numbers have been filled in.
Solution:
|4,781 | |
|7,652 |
Example
|7,642 |7,643 |
|7,652 |
Solution
• Activity 11: Give the students situations such as this while playing Spin and Win:
You had written _ _ 6 _ 2 _ and on your next spin you got a 7, where would you place the 7? Why did you make that choice?
-----------------------
Grade 4
Mathematics
30,000 + 2,000 + 600 + 4
Thirty-two thousand, six hundred four
32, 604
35,604
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hÒp 5?\?huUhÒp 5?\?h9%Õhw9™5?B*[pic]\?phhw9™5?B*[pic]\?phhw9™hw9™5?PJaJhw9™5?thirty-five thousand, six hundred four
30,000+5,000+600+4
61,215
sixty–one thousand, two hundred fifteen
60,000+1,000+200+10+5
45,213
forty-five thousand, two hundred thirteen
40,000+5,000+200+10+3
34,687
32,564
45,459
45,238
................
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