2005 – 2006
Everett Public Schools
1
K – 5 End of the Year Computation Targets
Following are Everett’s end of the year recall targets in computation. The recall of basic facts is important so students’ performance and accuracy are
not impacted when doing more sophisticated mathematical problems later in their school career and it is embedded in the document below.
When reviewing these targets please keep in mind that
recall is one of many components demonstrating mathematical performance
. Students’
success in mathematics is also very dependent on their being able to utilize these facts in problem solving situations, which is not assessed through
recall tasks. Basic fact practice is essential in reaching these targets and is found throughout each unit and within the Classroom Routines (K-2) and
daily 10 Minute Math (3-5) ongoing practice. (Adapted from Mercer Island SD)
K – 2
3
4
5
End of the Year Recall
Expectations of Basic Facts
We want our students to develop a solid conceptual
understanding of the mathematical operations before
placing emphasis on recall. Thus we have K-2
computation expectations in order to allow for the
development of these concepts.
By the end of second grade the goal is for all students
to:
Compute addition and subtraction to 10+10 with
fluency.
Recall basic addition and subtraction facts to 10: 20
facts in 1 minute, 90% accuracy.
Recall of multiplication
facts 0 -10 ( or Array set
A):
50 facts in 3 minutes, 90%
accuracy
Recall of addition facts to
10+10:
30 facts in 2 minutes, 90%
accuracy
Recall multiplication/division
facts 0 – 12: 60 facts in 3
minutes, 90% accuracy
(Array sets A and B)
Recall
multiplication/division
facts 0 – 12: 80 facts in 3
minutes, 90% accuracy at
the beginning of the year.
Practice these facts
throughout the year to
maintain fluency.
Multi-digit
Computation
without tools
By the end of second grade the goal is for all students
to:
Solve addition and subtraction problems with two- or
three-digit numbers (breaking apart into 100’s, 10’s
and 1’s), estimate with reasonableness
Competent with at least
two strategies for solving
each of the 4 operations up
to 3-digit and estimate
with reasonableness.
(Repeated addition should
rarely be used as a strategy
by the end of the year)
Competent with at least two
efficient
strategies for solving
each of the 4 operations up to
3-digit and estimate with
reasonableness.
Place Value
By the end of second grade the goal is for all students
to
:
Conservation of large numbers, working with 10’s and
1’s, and identifying place value (vocabulary)
Compare, order and represent numbers to 1,000
Conservation of large
numbers, working with
10’s and 1’s, landmarks in
the 100’s and identifying
place value
Compare, order, and
represent numbers to
10,000
Addition or subtraction of
non-negative fractions: up
to 3-like denominator
fractions.
Addition or subtraction of
non-negative decimals:
two numbers with
decimals to the 1000
th
place or with 3 decimals
to the 100
th
place.
Use the understanding of the
number system/properties to
solve larger problems.
Apply the concepts of odd
and even numbers to check
for divisibility
Finds factors and multiples to
help solve problems
Counting
By the end of second grade the goal is for all students
to:
Count on and count back.
Count by 2’s, 5’s, and 10’s.
Skip counting, counting
on/back, grouping by 2’s,
5’s, and 10’s
2005 – 2006
Everett Public Schools
2
CHILDREN’S STRATEGIES FOR SOLVING BASIC FACTS (MENTAL MATH)
PROBLEM
STUDENTS USE
COUNTERS
COUNTING
DERIVED FACTS
RECALL
5 + 7 = ?
Join Result
Unknown
Makes a set of 5 counters and a
set of 7 counters. Pushes the
two sets together and counts all
the counters.
Counts: “5 [pause], 6, 7, 8,
9, 10, 11, 12,” extending a
finger with each count. “The
answer is 12” [The counting
sequence may also begin
with the larger number]
“Take 1 from the 7 and
give it to the 5. That makes
6 + 6, and that’s 12.”
5 plus 7 is 12.
12 – 5 = ?
Separate
Result
Unknown
Makes a set of 12 counters and
removes 5 of them. Then
counts the remaining counters.
Counts back “12, 11, 10, 9,
8 [pause], 7. It’s 7.” Uses
fingers to keep track of the
number of steps in the
counting sequence.
“12 take away 2 is 10, and
take away 3 more is 7.”
12 take away 5 is 7.
4 + ? = 11
Join Change
Unknown
Makes a set of 4 counters.
Makes a second set of
counters, counting “5, 6, 7, 8,
9, 10, 11,” until there is a total
of 11 counters. Counts the 7
counters in the second set.
Counts “4 [pause], 5, 6, 7, 8,
9, 10, 11,” extending a
finger with each count.
Counts the 7 extended
fingers. “It’s 7.”
“4 + 6 is 10 and 1 more is
11. So it’s 7.”
4 and 7 make 11.
5 x 7 = ?
Makes 7 groups of 5 counters
and counts them all.
5, 10, 15, 20, 25, 30, 35
5 times 5 is 25 and 10 more
is 35.
5 times 7 is 35.
56
÷
8 = ?
Counts out 56 counters. Pulls
out groups of 8 until 7 groups
are made.
8, 16, 24, 32, 40, 48, 56
8 times 8 is 64. 8 less is 56.
So that’s 7.
8 x 7 is 56.
Adapted from: Carpenter, T.P., Fennema, E. & Franke, M.L. (1996). Cognitively Guided Instruction: A knowledge base for reform in primary mathematics instruction.
Elementary
School Journal
, 97, 3-20.
CHILDREN’S STRATEGIES FOR MENTAL MATH MULTI-DIGIT COMPUTATION
2005 – 2006
Everett Public Schools
3
STUDENTS USE COUNTERS
PROBLEM
COUNTING
BY 1s
BY 10s
BY 1s
BY 10s
ALGORITHMS
25 + 17 = ?
Makes the set of
25 by ones and a
set of 17 by ones
and counts them
all
Makes a set of 25
and a set of 17 by
using tens and
ones and counts
them all
Starts with 25,
counts by 1s,
keeping track of
how many are
added on until the
total is reached
e.g., 25, 26, 27, 28,
29, 30, 31….42
Starts with 25,
counts on by 10s.
e.g., 25, 35, 36,
37….42
20 and 10 is 30, 5 and 7 is 12.
30 and 12 is 42
OR
25 and 10 is 35 and 7 more is 42
OR
25 and 20 is 45, less 3 is 42.
47 – 28 = ?
Makes a set of 47
by ones and then
takes away 28 by
ones.
Makes a set of 47
by using tens and
ones and then
takes away 28.
Counts back from
47 by ones or
counts on from 28
until get to 47
Counts back from
47 by ones or
counts on from 28
by tens
40 take away 20 is 20. 8 take away 7
is 1. 20 take away 1 is 19
OR
47 take away 20 is 27. 27 take away
8 is 19.
OR
47 take away 20 is 17 plus two is 19.
12 X 15 = ?
Makes a set of 12
by ones and
repeats that 15
times. Counts
everything up.
Makes a set of 12
by using tens and
1s and repeats that
15 times. Counts
everything up.
SKIP COUNTS
12, 24, 36, 48 ……180
or adds 12, 15 times and figures out various
ways of adding the list up.
12 times 12 is 144. 12 times 3 is 36.
144 times 36 is 180.
OR
12 times 10 is 120. 12 times 5 is 60.
120 and 60 is 180.
OR
12 times 5 is 60. 60 times 3 is 180.
120 ÷ 15
Makes a set of
120 by ones. Pulls
out groups of 15
and counts how
many groups are
pulled out and
how many are left
over.
Makes a set of 120
by using 10s and
ones. Pulls out
groups of 15 and
counts how many
groups are pulled
out and how many
are left.
SKIP COUNTS
15, 30, 45, 60, 75, 90, 105, 120
or adds up 15 until get close to or to
120.
15 goes into 105, 7 times and 15
more is 120. That’s 8.
OR
15 times 4 is 60. 60 times 2 is 120.
That’s 8.
Adapted from: Carpenter, T.P., Fennema, E. & Franke, M.L. (1996). Cognitively Guided Instruction: A knowledge base for reform in primary mathematics instruction.
Elementary
School Journal
, 97, 3-20.
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