Grade 4
Mathematics
Table of Contents
Unit 1: Data, Graphs, and Numbers 1
Unit 2: Place Value, Number Sense and Measurement 15
Unit 3: Understanding Multiplication and Division 26
Unit 4: The Multiplication Algorithm 35
Unit 5: Dividing by 1-Digit Divisors 46
Unit 6: Geometry and Measurement 56
Unit 7: Fun with Fractions and Chance 71
Unit 8: Algebraic Thinking-Patterns, Counting Techniques, and Probability 80
Louisiana Comprehensive Curriculum, Revised 2008
Course Introduction
The Louisiana Department of Education issued the Comprehensive Curriculum in 2005. The curriculum has been revised based on teacher feedback, an external review by a team of content experts from outside the state, and input from course writers. As in the first edition, the Louisiana Comprehensive Curriculum, revised 2008 is aligned with state content standards, as defined by Grade-Level Expectations (GLEs), and organized into coherent, time-bound units with sample activities and classroom assessments to guide teaching and learning. The order of the units ensures that all GLEs to be tested are addressed prior to the administration of iLEAP assessments.
District Implementation Guidelines
Local districts are responsible for implementation and monitoring of the Louisiana Comprehensive Curriculum and have been delegated the responsibility to decide if
· units are to be taught in the order presented
· substitutions of equivalent activities are allowed
· GLES can be adequately addressed using fewer activities than presented
· permitted changes are to be made at the district, school, or teacher level
Districts have been requested to inform teachers of decisions made.
Implementation of Activities in the Classroom
Incorporation of activities into lesson plans is critical to the successful implementation of the Louisiana 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 Grade-Level Expectations 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.
New 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 http://www.louisianaschools.net/lde/uploads/11056.doc.
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 each 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. The Access Guide will be piloted during the 2008-2009 school year in Grades 4 and 8, with other grades to be added over time. Click on the Access Guide icon found on the first page of each unit or by going directly to the url http://mconn.doe.state.la.us/accessguide/default.aspx.
Louisiana Comprehensive Curriculum, Revised 2008
Grade 4
Mathematics
Unit 1: Data, Graphs, and 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. Types of graphs (bar, pictograph, line plot, line graph) are made and interpreted, comparing and contrasting the data involved. Number patterns, including input-output situations and odd and even 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 comparing large numbers to 1,000,000. They make, use, and interpret data from graphs and tables. They utilize number patterns to predict missing elements in a pattern and apply probability to real-life situations.
Guiding Questions
1. Can students show command of basic facts from grade 3?
2. Can students demonstrate an understanding of large numbers to 1,000,000?
3. Can students read, compare, and order large numbers to 1,000,000 using place value strategies?
4. Can students select and make appropriate graphs for data sets and graph input-output patterns?
5. Can students find the mean, median and mode for a small set of numbers when the answer is a whole number?
6. Can students investigate and determine patterns in operations on odd-even numbers and generalize?
7. Can students use data sets and graphs to answer real-life questions?
Unit 1 Grade-Level Expectations (GLEs)
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)
4. / Know all basic facts for multiplication and division through 12 x 12 and 144 ÷ 12, and recognize factors of composite numbers less than 50 (N-1-E) (N-6-E) (N-7-E)
12. / Count money, determine change, and solve simple word problems involving money amounts using decimal notation (N-6-E) (N-9-E) (M-1-E) (M-5-E)
13. / Determine when and how to estimate and when and how to use mental math, calculators, or paper/pencil strategies to solve multiplication and division problems (N-8-E)
14. / Solve real-life problems, including those in which some information is not given (N-9-E)
Data Analysis, Probability, and Discrete Math
34. / Summarize information and relationships revealed by patterns or trends in a graph, and use the information to make predictions (D-1-E)
35. / Find and interpret the meaning of mean, mode, and median of a small set of numbers (using concrete objects) when the answer is a whole number (D-1-E)
36. / Analyze, describe, interpret, and construct various types of charts and graphs using appropriate titles, axis labels, scales, and legends (D-2-E) (D-1-E)
37. / Determine which type of graph best represents a given set of data (D-1-E), (D-2-E)
39. / Use lists, tables, and tree diagrams to generate and record all possible combinations for 2 sets of 3 or fewer objects (e.g., combinations of pants and shirts, days and games) and for given experiments (D-3-E) (D-4-E)
40. / Determine the total number of possible outcomes for a given experiment using lists, tables, and tree diagrams (e.g., spinning a spinner, tossing 2 coins) (D-4-E) (D-5-E)
41. / Apply appropriate probabilistic reasoning in real-life contexts using games and other activities (e.g., examining fair and unfair situations) (D-5-E) (D-6-E)
Patterns, Relations, and Functions
42. / Find and describe patterns resulting from operations involving even and odd numbers (such as even + even = even) (P-1-E)
43. / Identify missing elements in a number pattern (P-1-E)
44. / Represent the relationship in an input-output situation using a simple equation, graph, table, or word description (P-2-E)
Sample Activities
Activity 1: Develop a Sense of Large Numbers (GLEs: 2, 13, 14)
Materials List: clock, calculator, How Much is a Million? by David Schwartz, estimation materials, (e.g., beans on the overhead, dots that can be drawn in one minute, 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. Then 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) X (Number of servings) = (Estimated amount of items in the container).
Activity 2: Just a Grain of Rice (GLEs: 2, 13, 14, 42, 43, 44)
Materials List: rice, spoon, jar, calculator, pencil, overhead, One Grain of Rice by Demi, or The King’s Chessboard by David Birch, Grain of Rice BLM
As an introduction to this book, show the students a spoonful of rice. Have them write down their estimate of the number of grains of rice in the spoon. Pour the rice on the overhead. Put the rice into estimated groups of 20 grains. Count by 20’s the groups of rice. Compare the students’ estimated amounts of rice to the estimated amounts of rice on the overhead. Repeat this activity using the spoon of rice as the new benchmark to fill a small 3 ounce paper cup. Were the estimates closer this time? Why or why not?
Read either One Grain of Rice by Demi, or The King’s Chessboard by David Birch. Have students use a calculator to determine the amount of rice that is received each day. Extend the activity by having students use a calculator to complete an input output table for each of the 31 days using the Grain of Rice BLM to discover the growing amounts of grains of rice discussed in either book. Through this activity, have them identify the odd and even number patterns that result from adding or multiplying numbers.
Activity 3: If You Made a Million! (GLEs: 2, 4, 12, 14)
Materials List: resources to find costs of items, (newspapers, magazines, or Internet access), calculator, pencil, paper, If You Made a Million by David M. Schwartz (optional)
Students will create a story chain (view literacy strategy descriptions). Story chains are especially useful in teaching math concepts, while at the same time promoting writing and reading. Students can be creative and use information and math from their everyday life. To create this story chain, put students in groups of four. On a sheet of paper, ask the first student to write the opening sentence of the Math Chain Story, “If I had a Million Dollars I would...” (The first student will put what they would do or buy and how much it would cost.) The second student would use the calculator and subtract that amount. Next, he/she would continue the story by adding what they would do/buy. The third and fourth persons would do the same. They will continue in this manner until there is no more money. The students may use newspapers, magazines, or the computer to find the costs of different items they would buy “if they made a million.”
Optional: Read and discuss the book, If You Made a Million by David M. Schwartz. (This book describes the various forms money can take, including coins, paper money and personal checks and how money can be used to make purchases, pay off loans, or build interest in a bank.)
Activity 4: Reach the Target Calculator Game (GLEs: 2, 42, 43)
Materials List: calculators, math learning log, pencil
Use the calculator to introduce counting large numbers. Have students enter 10,000 (100,000 or any large number as a starting point) on the calculator, press (or, or , or , etc.) depending on the target number, then press =. Ask them to continue to hit the equal sign to make the number grow. Choose any large number (the target number). Tell the students what number to start on and what number to put in to count by (, or, or , or , etc.) When everyone is ready, tell them to begin. The students race to see who reaches the target number first (e.g. the first one to get to 10, 672). Have students record any findings or observations made about these number patterns in their math learning log, (view literacy strategy descriptions). Each student should have a notebook specifically for writing math learning logs. Have them describe any number patterns they notice. For example:
· If you start with an even number and put in + 2, all the numbers are even.
· If you start with an odd number and put in + 2, all the numbers are odd.
· If you start with a number that is a multiple of 5, when you put in + 5, you have numbers that are multiples of 5 and all the numbers will end in either a 5 or 0.
· If you start with a number that ends in 0 and put in + 10, you will have numbers that are multiples of 10..
· Numbers that end in 2, 4, 6, 8, 0 or 5 have a factor of 2, 5, or 10; therefore, they will all be composite numbers except the number 2. (2 is the only even prime number.)
Activity 5: King of the Hill (GLEs: 2, 4, 42, 43)
Materials List: calculators
A calculator is used to play this game which provides practice in reading and comparing large numbers. Ask the students to begin by entering into the calculator any hundreds number (100, 200, 300, etc.) or thousands number (1000, 2000, 3000, etc.) or ten thousands number, (10,000, 20,000, 30,000, et.) that you have chosen. Have students press, (or, or , or , etc.), and then press the =. When everyone has completed the above task, ask students to place their elbows on their desks and their pointer finger in the air. Say, “Go!” and have the students press the = sign until you say, “Stop!” Ask one student to read his/her number. The next student challenges the first by reading his/her number. The student with the larger number remains standing. Continue with this comparison of numbers until there is only one person standing (The King/Queen of the Hill). Point out that the numbers that appear on the display bar on the calculator are multiples of the number you are skip counting by. (Notice the number patterns of multiples of 2 are even numbers, multiples of 5 end in either a 5 or 0, multiples of 10 end in 0. Numbers that have 2, 5, or 10 for a multiple will always be a composite number.)