4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Anchor Standard/Mathematical Practice(s)
MP.2. Reason abstractly and quantitatively. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure.
Information Technology Standard
Use technology tools and skills to reinforce classroom concepts and activities.
Revised Bloom's Level of thinking
Remembering Understanding Applying
Learning Target/Task Analysis
4.NBT.4 Students build on their understanding of addition and subtraction, their use of place value and their flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place value in describing and justifying the processes they use to add and subtract. This standard refers to fluency, which means accuracy and efficiency (using a reasonable amount of steps and time), and flexibility (using a variety strategies such as the distributive property, decomposing and recomposing numbers, etc.). This is the first grade level in which students are expected to be proficient at using the standard algorithm to add and subtract. However, other previously learned strategies are still appropriate for students to use. When students begin using the standard algorithm their explanation may be quite lengthy. After much practice with using place value to justify their steps, they will develop fluency with the algorithm. Students should be able to explain why the algorithm works. 4.NBT.5 Students who develop flexibility in breaking numbers apart (decomposing numbers) have a better understanding of the importance of place value and the distributive property in multi-digit multiplication. Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying whole numbers and use words and diagrams to explain their thinking. They use the terms factor and product when communicating their reasoning. Multiple strategies enable students to develop fluency with multiplication and transfer that understanding to division. Use of the standard algorithm for multiplication and understanding why it works, is an expectation in the 5th grade. This standard calls for students to multiply numbers using a variety of strategies. 4.NBT.6 In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context. Examples: A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the boxes so that each box has the same number of pencils. How many pencils will there be in each box? Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups. Some students may need to trade the 2 hundreds for tens but others may easily recognize that 200 divided by 4 is 50. Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4) Using Multiplication: 4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65 Common Misconceptions: (4.NBT.4-6) Often students mix up when to 'carry' and when to 'borrow'. Also students often do not notice the need of borrowing and just take the smaller digit from the larger one. Emphasize place value and the meaning of each of the digits. Specific strategies or students having difficulty with lining up similar place values in numbers as they are adding and subtracting, it is sometimes helpful to have them write their calculations on grid paper. This assists the student with lining up the numbers more accurately. If students are having a difficult time with a standard addition algorithm, a possible modification to the algorithm might be helpful. Instead of the 'shorthand' of 'carrying,' students could add by place value, moving left to right placing the answers down below the 'equals' line.
I can...
I can add multi digit whole numbers. I can subtract multi digit whole numbers. I can multiply a whole number of up to four digits by a one digit number. I can multiply a two digit number by a two digit number. I can illustrate my multiplication calculations through a variety of methods. I can divide up to four digits by one digit using various methods. I can recognize the relationship between multiplication and divison.
Essential Vocabulary
add, subtract, multiply, equations, rectangular arrays, area models, product, quotients, remainders, dividends, divisors, multiplication, division, equations, rectangular arrays, area models
Sample Assessments
8 x 8,256 87 x 36 Students will measure the length and width of the classroom and then multiply the dimensions to find the area. Repeat in the hall, the cafeteria, and the playground. Determine the proper unit of measurement to use in each case.
Each year our school has a field day where students rotate between 7 different activities. If the physical education teacher divides the 434 students evenly between the activities, how many students will there be at each activity? Will there be any students left out? Justify your answer.
Common Core Standards
4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
4.NBT.6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Anchor Standard/Mathematical Practice(s)
MP.2. Reason abstractly and quantitatively.MP.3. Construct viable arguments and critique the reasoning of others.
MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.7. Look for and make use of structure.
Information Technology Standard
Use technology tools and skills to reinforce classroom concepts and activities.Revised Bloom's Level of thinking
RememberingUnderstanding
Applying
Learning Target/Task Analysis
4.NBT.4Students build on their understanding of addition and subtraction, their use of place value and their
flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place
value in describing and justifying the processes they use to add and subtract.
This standard refers to fluency, which means accuracy and efficiency (using a reasonable amount of
steps and time), and flexibility (using a variety strategies such as the distributive property,
decomposing and recomposing numbers, etc.). This is the first grade level in which students are
expected to be proficient at using the standard algorithm to add and subtract. However, other
previously learned strategies are still appropriate for students to use.
When students begin using the standard algorithm their explanation may be quite lengthy. After much
practice with using place value to justify their steps, they will develop fluency with the algorithm.
Students should be able to explain why the algorithm works.
4.NBT.5
Students who develop flexibility in breaking numbers apart (decomposing numbers) have a better
understanding of the importance of place value and the distributive property in multi-digit multiplication.
Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying
whole numbers and use words and diagrams to explain their thinking. They use the terms factor and
product when communicating their reasoning. Multiple strategies enable students to develop fluency with
multiplication and transfer that understanding to division. Use of the standard algorithm for multiplication
and understanding why it works, is an expectation in the 5th grade.
This standard calls for students to multiply numbers using a variety of strategies.
4.NBT.6
In fourth grade, students build on their third grade work with division within 100. Students need
opportunities to develop their understandings by using problems in and out of context.
Examples:
A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the
boxes so that each box has the same number of pencils. How many pencils will there be in each box?
Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal
groups. Some students may need to trade the 2 hundreds for tens but others may easily recognize
that 200 divided by 4 is 50.
Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4)
Using Multiplication: 4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65
Common Misconceptions: (4.NBT.4-6)
Often students mix up when to 'carry' and when to 'borrow'. Also students often do not notice the
need of borrowing and just take the smaller digit from the larger one. Emphasize place value and
the meaning of each of the digits.
Specific strategies or students having difficulty with lining up similar place values in numbers as
they are adding and subtracting, it is sometimes helpful to have them write their calculations on
grid paper. This assists the student with lining up the numbers more accurately.
If students are having a difficult time with a standard addition algorithm, a possible modification
to the algorithm might be helpful. Instead of the 'shorthand' of 'carrying,' students could add by
place value, moving left to right placing the answers down below the 'equals' line.
I can...
I can add multi digit whole numbers.I can subtract multi digit whole numbers.
I can multiply a whole number of up to four digits by a one digit number.
I can multiply a two digit number by a two digit number.
I can illustrate my multiplication calculations through a variety of methods.
I can divide up to four digits by one digit using various methods.
I can recognize the relationship between multiplication and divison.
Essential Vocabulary
add, subtract, multiply, equations, rectangular arrays, area models, product, quotients, remainders, dividends, divisors, multiplication, division, equations, rectangular arrays, area modelsSample Assessments
8 x 8,256
87 x 36
Students will measure the length and width of the classroom and then multiply the dimensions to find the area. Repeat in the hall, the cafeteria, and the playground. Determine the proper unit of measurement to use in each case.
Each year our school has a field day where students rotate between 7 different activities. If the physical education teacher divides the 434 students evenly between the activities, how many students will there be at each activity? Will there be any students left out? Justify your answer.
Differentiation
Intervention:
Use base ten blocksUse a deck of cards to practice place value, making biggest/smallest number, etc.
http://daretodifferentiate.wikispaces.com/Choice+Boards
Enrichment:
Math24 game cardshttp://www.prongo.com/math/multiplication.html
Long Division
Instructional Resources
Place value manipulatives (e.g. money, base ten blocks, discs, etc.) and graph paper
http://nrich.maths.org/6402
http://www.kidsnumbers.com/long-division.php
Use Unit 4 at: http://eduplace.com/math/mthexp/g4/mathbkg/
http://nrich.maths.org/6402
Notes and Additional Information