word problems

Report
Teaching and Understanding Addition
and Subtraction in CCSS
Avoca School District 37
Jenn Rachmiel ([email protected])
Josh Minsley ([email protected])
Goals for Today
1. Where are the word problems in CCSS?
2. Explore the progression of addition and
subtraction in grades k - 5.
3. Make sense of the structure of word problems.
4. Connect word problems with algebraic
equations.
5. Explore the use of context in daily lessons.
Where are Word Problems in the
standards?
Kindergarten
CCSS.Math.Content.K.OA.A.2
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects
or drawings to represent the problem.
First Grade
CCSS.Math.Content.1.OA.A.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to,
taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by
using objects, drawings, and equations with a symbol for the unknown number to represent the
problem.
Where are Word Problems in the
standards?
Second Grade
CCSS.Math.Content.2.OA.A.1
Use addition and subtraction within 100 to solve one- and two-step word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all
positions, e.g., by using drawings and equations with a symbol for the unknown number to represent
the problem.
CCSS.Math.Content.2.MD.B.5
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the
same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the
unknown number to represent the problem.
CCSS.Math.Content.2.MD.C.8
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢
symbols appropriately.
Where are Word Problems in the
standards?
Third Grade
CCSS.Math.Content.3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for
the unknown number to represent the problem.
CCSS.Math.Content.3.OA.D.8
Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.
Where are Word Problems in the
standards?
Fourth Grade
CCSS.Math.Content.4.OA.A.2
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings
and equations with a symbol for the unknown number to represent the problem, distinguishing
multiplicative comparison from additive comparison.
CCSS.Math.Content.4.OA.A.3
Solve multistep word problems posed with whole numbers and having whole-number answers using
the four operations, including problems in which remainders must be interpreted. Represent these
problems using equations with a letter standing for the unknown quantity. Assess the reasonableness
of answers using mental computation and estimation strategies including rounding.
Where are Word Problems in the
standards?
Fourth Grade
CCSS.Math.Content.4.NF.B.3.d
Solve word problems involving addition and subtraction of fractions referring to the same whole and having
like denominators, e.g., by using visual fraction models and equations to represent the problem.
CCSS.Math.Content.4.NF.B.4.c
Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction
models and equations to represent the problem.
CCSS.Math.Content.4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes,
masses of objects, and money, including problems involving simple fractions or decimals, and problems that
require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement
quantities using diagrams such as number line diagrams that feature a measurement scale.
Where are Word Problems in the
standards?
Fifth Grade
CCSS.Math.Content.5.NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including
cases of unlike denominators.
CCSS.Math.Content.5.NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including
cases of unlike denominators, Use benchmark fractions and number sense of fractions to estimate mentally
and assess the reasonableness of answers.
CCSS.Math.Content.5.NF.B.3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems
involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
What are the Problem Solving
Structures?
● Buried on page 88 of the CCSS Glossary
● Research is long & complex
● Common threads:
o Mathematical actions
o Distinction between addition and subtraction
situations
● Most important- all situations involve three quantities,
and all three quantities can be unknown
● For more information...
Why do we need the Problem Solving
Structures?
● Exposure of how addition and subtraction is used in
various situations
● Emphasis on concepts vs tricks
● Interrelatedness of addition and subtraction
● Introduction to algebraic thinking at an early age
● Multiple approaches
How do the Structures Build?
Kindergarten
●
●
●
Within 10
Add to & Take From: Result Unknown,
Put together/Take Apart: Total Unknown, Addend Unknown
First Grade
●
●
Within 20
All Structures, all unknowns
Second Grade
●
●
Within 100
One and two step problems
How do the Structures Build
Third Grade
●
●
Time intervals
Four operations
Fourth Grade
●
●
Distances, liquid volumes, masses of objects, and money
Involving simple fractions or decimals
Fifth Grade
●
Fractions with unlike denominators
Addition/Subtraction Problem Solving Structures
“Active”
“Passive”
Let’s sort the word
problems!
Use the blank grid and the word problems to
determine what category each word problem
is in
“ Active” word problems
(Adding To)
(Taking From)
blue = Taught in kindergarten
“ Passive” word problems
(Taking Apart and
Putting Together)
Now go back to your district, and analyze
your text
Identifying what structures you have and/or missing
Using the blank problem solving structures grid tally the
types of word problems that currently exist within a
curriculum.
Rewrite existing problems
Write your own problems

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