Math week 6
Indicator
4.NBT.4
1.4.C.4 Fluently add and subtract multi-digit whole numbers using the
standard algorithm
Big Rocks
Week 6
● Determine a reasonable answer and choose a strategy to fluently
solve multi-digit subtraction problems (with or without decomposing
across zeroes)
● Add and subtract multi-digit numbers fluently
Upcoming: Week 7
● Represent and solve multi-step addition and subtraction word problems
● Focus on estimation as a way to determine reasonableness
Possible
learning
experiences
Subtract multi-digit numbers (decomposing across zeroes) using
the standard algorithm
Present 3,802 - 1,735 = ? and ask: In what place value positions will
you need to decompose in order to subtract?
What might be a reasonable answer for this problem?
Model solving the problem using Base Blocks Subtraction
How can you decompose a ten when there is a 0 in the tens place
(e.g., Decompose a hundred into 10 tens, and then decompose one of
the tens into 10 ones.) As the hundred block is moved into the tens
place and the tens block is moved into the ones place, what do the
small blue numbers represent on the standard algorithm to the right of
the blocks?
Lead a discussion of the place value generalizations that help
students subtract (e.g., You need to know the relationship between
place value positions and composing and decomposing groups of ten.
If you don’t have enough hundreds to subtract, you need to
decompose a thousand into 10 hundreds. If you have to decompose
across a zero, you might have to decompose a hundred thousand into
10 ten thousands and a ten thousand into 10 thousands)
Complete Subtract Across Zeroes using the standard algorithm. As
they work, ask them to explain the decomposing and the steps in the
standard algorithm using place value understandings.
Determine a reasonable answer and choose a strategy to fluently
solve multi-digit subtraction problems
Present horizontally the equation 120,000 – 111,953 = ? and lead
discussion: Without computing, how could you determine the number
of digits? e.g., 11 ten thousands from 111,953 need to be subtracted from
12 ten thousands in 120,000. But because of all the zeroes in 120,000, the
remaining ten thousand needs to be decomposed in order to subtract the
thousands, hundreds, tens, and ones, so there will be 4 digits in the
difference. Why might you want to consider the value of each number in the
equation and determine the number of digits in the difference before solving
(e.g., By thinking about the value of each number in the equation, I will know
what is and is not a reasonable answer).
Complete Sorting Differences and then reason with place value
understandings to sort these equations by the number of digits in each
difference without solving the equation.
Why it might be helpful to think about the number of digits in each
equation before solving? (e.g., When I started thinking about the
values of the numbers and the number of digits in the differences for I,
J, K, and L, I noticed that it was more efficient to solve them
mentally instead of using the standard algorithm)
Note to Teacher: Equations presented horizontally encourage students
to reason about the relative size of each number in the equation.
Subtract multi-digit numbers (with or without decomposing
across zeroes
? = 800,003 - 799,995. Engage students in thinking about place
value as well as the relationship between addition and subtraction by
asking: How could you solve this subtraction problem using
mental math?
Focus on reasoning about place value and addition to complete
the problem by determining which values belong in the hundreds,
thousands, ten thousands, and hundred thousands places of the
addends and sum - Use Subtracting Across Zeros again and ask pairs
to discuss before solving the problems: Which problem would you
solve using a method other than the subtraction algorithm and
why.
Add and subtract multi-digit numbers fluently
Present the problem on Page 2 of Flip- Reconstructing Problems and
ask: What do you notice ?(e.g., Only the tens and ones of the addends
and the sum are shown in the problem; the other digits are missing.)
Explain that the number strips will be used to put together an addition
problem that has been taken apart.
Lead the class in reasoning about place value and addition to
complete the problem by determining which values belong in
In which order did you determine the digits in the problem.
Focus on how might thinking about the relationship between
addition and subtraction help you place the digits.
Show ‘Tis Unique Page 1 Explain to students that all ten digits (0–9) are
used once in the problem and ask: What do you notice about the
problem and what was your reasoning for placing 7 in the hundreds
place in the top addend?
Show Tis Unique Page 2 where students determine the difference in a
subtraction problem in which a 4-digit number is subtracted from a 4digit number.
While students work, ask questions that will engage them in reasoning
about place value understandings (e.g., How did thinking about
whether you needed to decompose help you determine this
missing digit in this place?)
Possible
assessments
Determine a reasonable answer before computing
1.
Give students an addition problem.
2.
Ask: What might be a reasonable answer to the problem?
Prompt: How did you get that?
Proficiency: Students must use academic vocabulary, including:
benchmark, midpoint, rounding, estimate and place value.
3.
Solve and explain the problem.
Proficiency: Explanations must include and understanding of place
value and academic vocabulary, like: ones, tens, hundreds and
compose.
4.
Revisit estimation- Is your answer reasonable based on your
estimation? Why? (Prompt student to explain why numbers are off if
necessary)
Subtract Across Zeroes
Present 3,802 – 1,735 = ? and ask: What might be a reasonable answer for
this problem (e.g., 3,802 is about 2,000 more than 1,735, so a difference a bit
more than 2,000 would be reasonable.)
Reason about the number of digits in the sum or difference before
computing
Sorting Differences
Accurately add and subtract
Page 2 of Reconstructing Problems
Explain that the number strips will be used to put together an addition
problem that has been taken apart. Lead a discussion about the values in the
ones
and tens place that have already been placed in the sum (e.g., It doesn’t
matter if the 6 or the 7 is in the ones place of the first addend or if there are 5
tens
or 2 tens in the first addend.)
Choose from a collection of efficient methods, including the standard
algorithms, depending on the numbers in the problem
Subtract Across Zeroes
Present the problem ? = 800,003 − 799,995. Engage students in thinking
about place value as well as the relationship between addition and
subtraction by
asking: How could you solve this subtraction problem using mental math
Justify why a computation strategy (e.g., standard algorithm,
compensation, adding up to find a difference) was selected and explain
why that strategy is efficient for the problem
Sorting Differences
When I notice that I need to decompose a ten thousand, a thousand, a
hundred, and a ten just to subtract, I might choose another strategy; I could
adjust
120,000 to 119,999, subtract, and then add 1 to the difference to
compensate.