West-Orange Cove ISD3rd Grade Mathematics – 6th Six Weeks2012 - 2013
Week 1Apr 29 – May 1 / Learning Standards
4.1 Use place value to represent whole numbers and decimals.
4.3 Add and subtract to solve meaningful problems involving whole numbers and decimals.
4.5 Estimate to determine reasonable results.
4.10 Recognize the connection between numbers and their properties and points on a line.
4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.
4.15 Communicate about Grade 4 mathematics using informal language.
4.16 Use logical reasoning.
Reporting Category 1 / Major Concepts:
- Place Value
- Value of digits depends on the place in the number
- Addition and subtraction are connected. Addition names the whole and subtraction names a missing part.
- Compare and order numbers
- Problem Solving Model
- Thinking about learning and making connections
- Use accountable talk by using the language of mathematics
- Using Base 10 to represent numbers
Instruction / Resources / Math Stations / Assessment
The last six weeks is dedicated to teaching and preparing students for fourth grade. Reporting Category 1: Numbers, Operations, and Quantitative Reasoning. It is important to remember that throughout the year problem solving should be taught using a multitude of problems including skills from all categories to include measurement (time, temperature, area, and perimeter). TEKS 4.l4 – 4.16 should be taught daily and incorporated into Math Stations. Students must also be able to identify the mathematics in everyday situations. This will involve understanding the problem, planning a method for solving, solving, and assessing the reasonableness of the solution.
Bring meaningful examples of the world around them into the classroom to make it meaningful. For example, the number of students in each class, in each grade level, the number of white milk served each day, the number of chocolate milk served each day, the number of hours and minutes students have spent in school, etc. Write problems and stories with these numbers. Challenge students to find examples and share. You can graph the examples, compare the numbers, etc. The key is to bring math into the classroom that the students can relate to and to help them get excited about the math. Share your excitement with the students.
Students have a difficult time conceptualizing large numbers. Use examples they are familiar with, i.e. there are 1256 students in this school. 2562 people attended the high school football game. Connect large numbers with literature for example, “How Much is A Million” or “If You Made A Million”. Connect the literature and explorations to place value. To help students develop large number concepts.
Key Vocabulary: digit, place value, standard form, expanded form, word form, compare, order, less than, greater than, equal to, compose/ decompose numbers, range, mean, median, mode
Problem Solving Strategy: Make an organized list – this strategy is used when finding combinations of two or more items. Students should use a systematic method or writing the list rather than a random list. Explain and provide examples of each when teaching this strategy.
Place Value:
Teacher should use base 10 blocks to ensure students have a concrete grasp of our number system. Explain in detail the place value system using base ten. (TE Topic 1 2E).
Model several numbers using base 10 blocks. Have student volunteers to model given numbers using the base 10 blocks as well.
Connect this learning to the number of the week and practice writing multiple representations of the numbers in expanded form and written form.
Example:
Relate patterns in model to place value chart.
Example:
Relate patterns in models to similar patterns in standard and word form of whole numbers.
Groups of three digits (periods)
Commas between periods
Ones, tens, hundreds repeated
in each period
Comma follows the name of
each period in word form
Ask the students, “How can the number one million, six thousand, three hundred eighty-nine be written in standard form?” Prompt the students to place the digits in the appropriate period and then combine the periods to form the whole number.
Millions / Word Form
H / T / O / One million,
0 / 0 / 1
Thousands / Word Form
H / T / O / Six thousand,
0 / 0 / 6
Units / Word Form
H / T / O / Three hundred eighty-nine,
3 / 8 / 9
Answer: 1,006,389
Describe the value of each digit in a whole number.
Use an instructional strategy such as a place value chart to determine the value of each digit within a number.
Example:
Ask the students, “What is the value of the digit 7 in the number 2,075,361?” Prompt the students to place the digits
of the number 2,075,361 in each digit’s correct place on the place value chart.
Millions / Thousands / Units
H / T / O / H / T / O / H / T / O
2 / 0 / 7 / 5 / 3 / 6 / 1
Answer: The 7 is in the ten thousands place. It has a value equal to 70,000.
Use expanded notation to represent numbers and the
individual values of digits within a number.
Example:
Ask the students, “How can the number 8,205,039 be represented in expanded notation?” Prompt the students to use 1” grid paper to represent the number 8,205,039 in expanded notation.
Answer:
8,000,000 + 200,000 + 5,000 + 30 + 9
Compare and order whole numbers through the millions
place. Use symbols such as <, >, and = to compare umbers.
Example:
Ask the students, “Which number is greater: 1,238,765 or 1,283,765?” Prompt the students to line up the numbers vertically in a place value chart.
Millions / Thousands / Units
H / T / O / H / T / O / H / T / O
1 / 2 / 3 / 8 / 7 / 6 / 5
1 / 2 / 8 / 3 / 7 / 6 / 5
Prompt the students to compare the largest place values of each number in order to determine which number is
greater. The digits in the millions place and the hundred thousands place both have the same value. The second number has a greater value in the ten thousands place. Therefore, the second number is greater than the first number. Answer: 1,283,765 > 1,238,765
Ask the students, “How can the numbers 235,859; 362,262; and 253,859 be arranged in order from greatest to least?”
Prompt the students to line up the numbers vertically in a place value chart to determine the number with the greatest value.
Thousands / Units
H / T / O / H / T / O
2 / 3 / 5 / 8 / 5 / 9
3 / 6 / 2 / 2 / 6 / 2
2 / 5 / 3 / 8 / 5 / 9
Possible Answer:
“The number 362,262 is the largest number because it has the largest value in the hundred thousands place. The
number 253,859 is the second largest number because it has a larger value in the ten thousands place than the
number 235,859.”
Answer: 362,262; 253,859; 235,859 / enVision Math -Topic 1
Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:
enVision eTools
Manipulative -Base ten blocks, counters, dice
/ Number fluency – addition and subtraction – use a mix of timed drills and computation
Problem Solving – word problems involving place value and addition and subtraction. Also include problems students can solve by making an organized list.
Journal writing – the importance of place value
Number of the week
Measurement Station
Interventions/Extensions
Based on student needs
Addition and subtraction with regrouping. Continue using base ten blocks or counters if necessary when problem solving.
Relating place value to base 10. Each student will make a place value foldable. Next provide students with baggies containing a different number of counters. Each member of the group will count the contents of their baggie and record the total. Next students pass their baggie to the right and repeat the process. Students then add the total number of all the baggies using base 10 blocks and their foldable. To extend this activity and check for understanding, ask students to subtract certain amounts.
Comparing whole numbers. To compare whole numbers struggling students can use a place value chart. They write each number in the chart then find the greatest or smallest number. Provide explicit instruction in the use of the greater than and less than symbols.
Students that are ready to move ahead can Race to a million. Students work in pairs or small groups and take turns rolling 3 dice. Students can then make any number they want using the three numbers. Each time they take a turn they add their numbers to keep a running total. The first one to reach a million wins.
GT: Stretch students thinking to think of representing numbers in different forms. (E 2H) Example: 23,000 can be 23 thousands, 230 hundreds, 2,300 tens or 23,000 ones.
Others numbers to provide students: 56,000; 893; 435,678.
GT Book Project. / Formal or informal place value of whole numbers, comparing and ordering whole numbers and problem solving.
Product/Project
Foldable – place value chart
Frayer model with vocabulary term – Place Value
Concept Map – Place Value
Week 2 & 3
May 6 – 10
May 13 – May 17 / Learning Standards
4.1 Use place value to represent whole numbers and decimals.
4.3 Add and subtract to solve meaningful problems involving whole numbers and decimals.
4.5 Estimate to determine reasonable results.
4.10 Recognize the connection between numbers and their properties and points on a line.
4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.
4.15 Communicate about Grade 4 mathematics using informal language.
4.16 Use logical reasoning.
Reporting Category 1 / Major Concepts
- Place value
- Addition
- Subtraction
- Rounding
- Ordering and comparing numbers
- Problem Solving Model
- Thinking about learning and making connections
- Use a number line
- Use accountable talk by using the language of mathematics
Instruction / Resources / Math Stations / Assessment
Key Vocabulary: digit, standard form, expanded form, word form, compare and order, problem solve, round numbers, less than, greater than, equal to, range, mean, median, mode
Problem solving strategy – Missing or extra information, drawing a picture
Use a problem-solving model to solve problems involving place value.
Use only the digits 1, 2, 3, 4, 5, and 6 to build the smallest 6-digit number with the 6 in the hundred thousands place
and the 4 with a value of 40. If each digit can only be used once, what number can be created?
Read and Understand:
Ask the students:
- To restate the problem in their own words.
- “What is the important information in this problem?”
- “What are we trying to find out?” “What do I know?
Plan and Solve:
Ask the students:
- “What strategy could we use to solve this problem?”
- “What operation should I use? Why?”
- “What is the answer?”
Look Back and Check
Ask the students:
- “Did I check my work?”
- Did I compare my work to the information in the problem to be sure I used the correct information?”
- “Is my answer reasonable?”
- “Did I answer the question?”
thousands place, the 2 in the thousands place, the 3 in the hundreds place, and the 5 in the ones place. The answer is
612,345.”
Possible Answer: “The number 612,345 satisfies all the criteria because it has the digit 6 in the hundred thousands
place and 4 in the tens place. It is the smallest number possible created by using the given set of digits.”
Use rounding to approximate reasonable results in addition and subtraction problem situations.
Example:
The Hammond City Symphony performed two concerts on Saturday. There were 4,364 people at the 2:00 P.M. concert and 7,639 people at the 7:00 P.M. concert. About how many
people attended the 2 concerts? Prompt the students to determine that they are being asked to combine quantities (addition). Prompt the students to determine that
4,364 is closer to 4,000 and that 7,639 is closer to 8,000.
4,000 + 8,000 = 12,000 people Answer: 12,000 is a reasonable estimate of the total attendance at the two concerts.
Example:
Using the information from the table below, about how many more students does Bellevue High School have enrolled than Fayetteville High School?
Student Enrollment
School / Number of Students Enrolled
Oyster Creek / 1,789
Bellevue / 2,898
Fayetteville / 1,805
Prompt students to determine that they are being asked to compare two quantities (subtraction). Prompt the students to determine that 2,989 is closer to 3,000 and 1,805 is
closer to 2,000. 3,000 – 2,000 = 1,000 students
Answer: 1,000 students is a reasonable estimate of the difference between the enrollments of the two schools.
Use addition to solve problems involving whole numbers.
Example:
In 1959, the population of Vernon County was 351,698. If the population has increased by 215,697, what is Vernon county’s current population?
Answer: 567,395 people
Use subtraction to solve problems involving whole numbers.
Example:
Ms. Griffin wants to purchase a used truck. A 2004 truck is listed for $21,699, and a 2005 truck is listed for $26,759. How much money will Ms. Griffin save if she buys the 2004
truck?
Answer: $5,060
Locate and name points on a number line using whole
numbers.
Example:
Which point on the number line best represents 188?
A number line should be displayed in the classroom and students should refer to it when rounding as well as naming, points. Some students may need to use the number line as a scaffolding tool for addition and subtracting, skip counting, and so on. / enVision Math -Topic 1 TE Lessons 2-2 through 2-3,2-5 through 2-8, 2-10
Technology: Pearson enVision link for animated introduction, journal writing, and review – copy and paste this link:
Manipulatives: Base ten blocks, linking cubes, tape measures, dice / Number fluency – addition and subtraction timed drills and computation
Problem Solving – word problems involving rounding, addition, subtraction and problem solving strategies make an organized list, missing or extra information, and drawing a picture.
Journal writing – explain how to round and how it helps you in problem solving
Number of the week
Measurement Station
Interventions/Extensions
Based on student needs
Addition and subtraction with regrouping. Students often have trouble regrouping whether they are adding or subtracting. Continue using a place value chart and base 10 blocks. In addition provide real world problems for them to solve such as estimating the number of connecting cubes it would take to equal their height. Next students measure how tall they are and use connecting cubes to equal their height. Add the total number of connecting cubes for the length of 4 4th graders.
Students proficient in addition and subtraction can research the distance from their city to Dallas, then Austin, and back home again. Students then draw a map of their route and the miles. Next have students to write a word problem for a peer to solve.
GT: Students will work on this for 2 weeks. Texas Factoid (Topic 2 P. 29). Students will make a map of the US (or download one). Students will identify El Paso, Texas, Orange, Texas, Los Angeles California, Orange, California, and Orlando, Florida. Students will then plan a trip by selecting two states to travel to and from. Students will calculate the distance for their round trip. To challenge students farther tell them they will be driving a Toyota Camry that gets 36 MPG. Have them to develop strategies to calculate the amount of gas required for their trip.
GT Book Project / Formal – enVision Math Assessment
Profile with students and track progress. Set goals and interventions based on results.
Products/Project
Problem solving poster
Journal reflection entry explaining their thought process in solving a specific problem
.
Week 4 – 5
May 20 – May 31 / Learning Standards:
4.4 Multiply and divide to solve meaningful problems involving whole numbers.
4.5 Estimate to determine reasonable results.
4.6 Use patterns in multiplication and division.
4.7 Use organizational structures to analyze and describe patterns and relationships.
4.14 Apply Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.
4.15 Communicate about Grade 4 mathematics using informal language.
4.16 Use logical reasoning.
Reporting Category 1 and 2 / Major Concepts:
- Multiplication
- Relationship between addition and multiplication
- Multiplication is a pattern
- Properties of Multiplication
- Problem solving model
- Use accountable talk by using the language of mathematics
- Multiplication can be represented by modeling the factors (arrays)
Instruction / Resources / Math Stations / Assessment
Key Vocabulary: array, product, factors, multiple, Commutative Property of Multiplication, Zero Property of Multiplication, Identity Property of Multiplication, Distributive Property, column, row
Students must understand, “groups of items as single entities while also understanding that a group contains a given number of objects.” (Van De Walle).
Students must internalize and be able to quickly recall facts. This is the basis for their math learning for the next several years. Students must understand the concept of multiplication as repeated addition. Teach them “tricks” like using the number line (skip counting), multiplication grid, finger method, etc. until they know the facts. Teach students to use the commutative property of multiplication. Using this property they only have to remember 42 facts. Because if they know that 6*7=42 then they also know that 7*6=42. Teach struggling students to use anchors. For example, if they know that 6*6=36 they can quickly add 6 to get the answer to 6*7.
There are four problem structures students should be familiar with to be efficient problem solvers.
- Equal groups: Whole unknown.
If oranges cost .10 each, how much will he pay for 5 oranges? (rate)