D183 - task three
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Designing Curriculum and Instruction
- D183 (task three)
1
Designing Curriculum and Instruction - D183
Task three
[Name]
Western Governors University
December 2, 2023
Designing Curriculum and Instruction
- D183 (task three)
7
Vertical Alignment
A.
1. Houghton Mifflin Harcourt: Math Expressions Common Core
•
current grade:
First Grade
•
unit of instruction:
Unit 8 - Two Digit Addition
•
standards that correspond to the prior grade or level:
Kindergarten -
CCSS.MATH.CONTENT.K.OA.A.1
Represent addition and subtraction with objects, fingers, mental images,
drawings1, sounds (e.g., claps), acting out situations, verbal explanations,
expressions, or equations.
•
standards that correspond to the current grade or level:
First Grade -
CCSS.MATH.CONTENT.1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction
within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 +
4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 -
1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g.,
knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but
easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 +
6 + 1 = 12 + 1 = 13).
•
standards that correspond to the next grade or level:
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.1
2. The learning progression across the three grades starts in Kindergarten -
learning the foundational skills for their education career. In Kindergarten,
students are learning the meaning of numbers - then working addition and
subtraction in with tactile items to represent the number / equation. This is the
part of number sense that is stored in their long term memory. Learning this and
mastering this - will only benefit students in their mathematics. Then, in First
Grade - students are adding and subtracting within 20 with fluency within 10. This
curriculum helps students learn strategies and tools to be fluent in addition within
10, which creates number sense and helps to add in teen numbers. In second
grade, they not only are adding and subtracting in higher numbers - up to 100,
they are also solving one and two step word problems using the number sense
that was built upon. They are learning from their kindergarten experience of
learning basic numbers and learning their amounts through tactile / visual
supports to then having that memory stored and able to add/subtract fluency.
Designing Curriculum and Instruction
- D183 (task three)
7
3. A potential gap would be not grasping the foundational skills and struggling
throughout first and second grade. Not understanding the foundational skills
could be due to attendance, behavioral issues, learning delays, disabilities, or
inadequate teaching style. If students in Kindergarten do not understand number
sense - then addition and subtraction will be very difficult for them to master and
then it will get them further behind.
4. To support the potential gaps in the current grade level - here are some
suggestions for improvements.
One improvement
would be to cover not only
adding and subtracting word problems within 20, but also within 50. In Second
Grade, they are going over word problems within 100; I think the jump from 20 to
100 is a big jump and is where students tend to struggle / create gaps in learning.
Adding content that allowed first graders to practice within 50 would help that
transition from first to second grade.
The second improvement
would be to
include a
First Grade Review
in the beginning of Unit 1 Lesson 1 in Second
grade, to give them a refresher and won’t feel so overwhelmed with all the new
information at the beginning of the year. This could help students gain confidence
and fill in learning gaps that they missed before. A teacher then could see what
students are missing - and use tier 2 / tier 3 groups to fill in those gaps during
W.I.N. time, as well as tier 1 whole group - on grade level content.
Horizontal Alignment
B.
1.
To ensure horizontal alignment of the curriculum resources for the unit -
Two
Digit Addition.
I would meet with my team during PLC before we taught the
curriculum, to see where strengths and weaknesses are with the units. As a 4th
year teacher - I have taught this curriculum for four years, but my seasoned
coworkers have more understanding on where students typically struggle and
how to provide interventions, activities, accommodations, etc. - to help with
success. As a team - we will decide what assessments, strategies, supports, and
lessons to ensure we touch the standards mentioned in A1. As a team we will
decide to use the tools - ten sticks and extra ones manipulatives in all first grade
classrooms. This helps with the understanding of place value - which will then
introduce teen numbers and addition. This is a tangible visual tool to help
understand two digit addition. We will also decide that Unit 8 is a unit where
students struggle and need help understanding
Two Digit Addition.
We will decide
as a team to stretch out this lesson to ensure student understanding. We will
include extra activities, tier 2 small groups, and pre/post lesson assessments to
keep data. As a team we will meet every week to review data and adjust
curriculum if needed.
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Designing Curriculum and Instruction
- D183 (task three)
7
2. The steps my team would take to ensure horizontal alignment of the
instructional strategies for the unit would be to first meet pre teaching of the
lesson, and come up with the teaching styles (whole group, guided practice,
independent practice, and the assessments), pace, and supplemental materials
to use. We will also come up with coordinating activities, centers, games, etc. to
use to help support each lesson in the Unit 8:
Two Digit Addition
. As a team - we
will decide that we will use the strategies, in this order: fingers, circle drawings,
math mountains, and counting on. We will start at fingers and ultimately have
them counting on - to help support them in those two digit numbers without
having to use fingers or drawings/math mountains. If students are struggling -
then we will redirect them to using the strategies. We will then come together -
post teaching of the lesson, to compare thoughts and struggles during the
lessons. We can then decide if we are ready to continue to the next lesson, or
need to readjust to teach the lesson in a different way.
3. The steps my team would take to ensure horizontal alignment of the
assessments for the unit would be first to take initial math assessments to see
what their skills are initially. We then would compare unit tests - to see if students
are ready to move on to the next lesson, or re-adjust our instruction to support
students in mastery. Students often have a hard time with word problems using
two digit numbers, that is in the Unit 8 assessment as well as a lesson within Unit
8. In the lesson post-assessment that goes over word problems with two digit
numbers - we will compare data to see what we can do to prepare students more
or if we need to make changes to instruction. We can bring in the ten sticks and
extra ones - to represent these teen numbers while reading the word problems.
Sometimes breaking apart the word problem and using tangible tools - helps the
learner understand teen number sense, The way we will continue to do things will
depend highly on student assessment scores. If we compare and notice that
students are doing poorly - we will then come up with the missing skills and
differentiate the lesson to better fit the students needs (tier 2 / tier 3).
C.
References
Kindergarten » Operations & Algebraic Thinking
. (n.d.). Common Core State
Standards Initiative. Retrieved December 2, 2023, from
https://www.thecorestandards.org/Math/Content/K/OA/
Designing Curriculum and Instruction
- D183 (task three)
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Grade 1 » Operations & Algebraic Thinking
. (n.d.). Common Core State
Standards Initiative. Retrieved December 2, 2023, from
https://www.thecorestandards.org/Math/Content/1/OA/
Grade 2 » Operations & Algebraic Thinking
. (n.d.). Common Core State
Standards Initiative. Retrieved December 2, 2023, from
https://www.thecorestandards.org/Math/Content/2/OA/