Grade 2 – Geometry
Essential Questions:
1. Why are geometry and geometric figures relevant and important?
2. How can geometric ideas be communicated using a variety of representations?
******(i.e maps, grids, charts, spreadsheets)
3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning?
Essential Vocabulary – shapes, attributes, angles, faces, triangles, quadrilaterals, pentagons, hexagons, cubes, plane shapes, trapezoid, circle,
rectangle, vertices, closed figure, partition, rectangle, square, row, column, tiles, area, equal shares, halves, thirds, whole, fourths, identical,
divide, fraction form
We want students to understand that geometry is all around us in 2 or 3D shapes. Geometric shapes have certain properties and can be
transformed, compared, measured, and constructed.
2.G.1: Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify
triangles, quadrilaterals, pentagons, hexagons, and cubes.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. the names of shapes (triangles,
1. what attributes determine a two or three
1. recognize specific
quadrilaterals, pentagons, hexagons, and
dimensional shapes.
attributes (such as number of angles or
cubes.)
faces)
2. the difference between two dimensional
2. draw specific attributes (such as number of
and three dimensional figures.
angles or faces)
3. what angles and faces are.
3. identify shapes (triangles, quadrilaterals,
pentagons, hexagons, and cubes)
2.G.2.: Partition a rectangle into rows and columns of same-size squares and
count to find the total number of them.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
1. that a rectangle can be divided into rows
1. that repeated rows and columns of equal
and columns.
sized squares will construct a rectangle.
Students will be able to…
1. partition a rectangle into same sized
squares.
2. count the squares to find the area.
2.G.3.: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of,
etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same
shape.
Students will know…
1. that circles can divided into equal parts
(halves, thirds, fourths)
2. that rectangles can divided into equal parts
(halves, thirds, fourths)
3. how to recognize one whole when written
in fraction form
Grade 2 Enduring Understandings
Students will understand…
1. circles and rectangles can be divided into
equal shares.
2. equal shares can be divided in different
ways.
Students will be able to…
1. divide a circle or a rectangles into halves,
thirds, and fourths.
2. read and write a fraction.
Grade 2 - Measurement
Essential Questions:
1. How does estimation help you find a reasonable measurement?
2. How do you determine the tool and unit to help you accurately measure?
3. When do you need to measure?
Essential Vocabulary –measure, length, ruler, yardstick, meter stick, measuring tape, unit, non-standard measurement, inches, feet, centimeters,
meters, estimate, length, difference, standard length unit, number line, analog clock, digital clock, a.m., p.m., dollar bills, quarters, dimes, nickels,
pennies, $, cents symbol, cents, line plot, horizontal scale, whole number, picture graph, bar graph, data, categories, put together, take apart,
compare
We want students to understand when to measure, what tool and unit to use, and how to use estimation to find a reasonable measurement.
2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to use a measuring tool to determine
1. when to choose the appropriate tool when
1. accurately measure length using a variety
length
measuring length
of tools
2. the difference between the metric and
2. differentiate between metric and standard
standard measurement systems
2.MD.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. they can measure length with nonstandard 1. that measurement results relate to the size
1. measure an object with two different units
objects (paper clips, unifix cubes, hands,
of the unit chosen (for example: it would
2. compare the different measurement results
etc.)
take more unifix cubes than hands to
2. how to compare two different units of
measure the length of a desk)
measurement
2.MD.3: Estimate lengths using units of inches, feet, centimeters, and meters.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
1. how to estimate length
1. which unit of measurement will result in a
2. inches, feet, centimeters, and meters
reasonable estimate
Students will be able to…
1. make a estimate of length
2. determine the difference between inches,
feet, centimeters, and meters
2.MD.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to measure length with standard units 1. that objects have different lengths that can 1. find the difference in length between two
2. how to compare length with standard units
be compared numerically
objects using standard units
3. how to find the difference between lengths
with standard unit.
2.MD.5: Use addition and subtraction within 100 to solve word problems within a cultural context, including those of Montana American Indians,
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.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to add and subtract (within 100)
1. how to apply addition and subtraction
1. solve addition and subtraction word
2. how to solve word problems involving
strategies to solve word problems
problems involving length
length, using different strategies
involving length
2. utilize different strategies for problem
3. Montana American Indians are a part of
2. math applies to the real world, including
solving
Montana culture
cultural components
2.MD.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,
..., and represent whole-number sums and differences within 100 on a number line diagram.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to horizontally represent numbers to
1. that a number line can be a tool for solving 1. build a number line with equally spaced
100 (number line diagram)
addition and subtraction problems
points to 100
2. how to use a number line to add and
2. add and subtract on a number line to 100
subtract numbers to 100
2.MD.7: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to tell time to the nearest five minutes 1. the life skill of being able to tell time on
1. tell and write time using analog and
2. how to write time to the nearest five
analog and digital clocks
digital clocks
minutes
2. tell and write time using a.m. and p.m.
3. how to tell time on both analog and digital
clocks
4. when to use a.m. and p.m.
2.MD.8: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you
have 2 dimes and 3 pennies, how many cents do you have?
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to count money
1. the life skill of being able to count money
1. count money
2. solve word problems involving money
2. the importance of recording money
2. solve money word problems and record the
3. use appropriate money symbols
accurately
answer appropriately
2.MD.9: Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of
the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to measure length
1. that a line plot is the precursor to a bar
1. collect and display data on a line plot
2. how to make a line plot
graph
2. the data can be displayed visually
2.MD.10: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set from a variety of cultural contexts, including those
of Montana American Indians, with up to four categories. Solve simple put together, take-apart, and compare problems using information
presented in a bar graph.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to draw a picture graph
1. how to utilize graphs for understanding
1. draw picture and bar graphs
2. how to draw a bar graph
data
2. use bar graphs to add, subtract, and
3. how to use a bar graph to add, subtract,
2. math applies to the real world, including
compare
and compare
cultural components
4. Montana American Indians are a part of
Montana culture
Grade 2 – Number Sense
Essential Questions:
1. Why do we use numbers, what are their properties, and how does our number system function?
2. Why do we use estimation and when is it appropriate?
3. What makes a strategy effective and efficient and the solution reasonable?
4. How do numbers relate and compare to one another?
Essential Vocabulary – digit, number(s), amount(s), hundreds, tens, ones, equals, bundle, place value, three-digit number, count, skip-count,
numbers, base-ten numerals, expanded form, compare, <, >, =, greatest, least, and smallest, addition, subtraction, sum, difference, operations,
properties, regroup, addend, fact family, number sentence, and number statement, column addition, written method, compose and decompose,
concrete models, mathematical drawings, mental math, communicate
We want students to understand that all numbers have value, uses, types, and we use operations and reasonableness to work with them.
2.NBT.1: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0
tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven,
eight, or nine hundreds (and
0 tens and 0 ones).
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. place value to the hundreds place
1. That digits have different amounts/values
1. understand place value
2. hundreds are represented by bundles of
depending on their place value (hundreds,
2. represent three digit numbers
tens
tens, and ones).
3. digits have different values depending
upon their place value
2.NBT.2.: Count within 1000; skip-count by 5s, 10s, and 100s.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
1. that patterns determine how to skip-count
1. that counting is sequential
(5s, 10s, 100s).
2. to apply patterns when skip-counting.
2. how to rote count, to 999 (from any
number).
*GFPS students will be able to count
backwards to 999 as well.
Students will be able to…
1. Count to 999 (from any starting point).
2. Skip-count by 5s, 10s, and 100s.
2.NBT.3.: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. number names
1. the placement of a digit dictates its value,
1. read and write numbers to 999 in both
2. base ten numerals (number system)
how it is read, and written.
expanded form and word name
3. expanded form
2.NBT.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the
results of comparisons.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. comparative symbols (<, >, and =).
1. the comparative relationship between
1. compare three-digit numbers.
2. how to compare three-digit numbers.
three-digit numbers.
2. use appropriate tools when comparing
3. how to record the results of comparing
numbers to 100-999(base-ten blocks,
numbers.
pictures, stamps,…).
2.NBT.5.: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between
addition and subtraction.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. fact families
1. there are multiple ways to solve addition
1. Add and subtract (based on place value
2. the basic facts fluently
and subtraction problems
and properties of operations)
3. different strategies for addition and
2. Use the relationship of fact families as a
subtraction
strategy for addition or subtraction
4. how to add and subtract to 99
2.NBT.6.: Add up to four two-digit numbers using strategies based on place value and properties of operations.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to add multiple (up to 4) two-digit
1. there are multiple ways to solve addition
1. add up to 4 two-digit numbers using a
numbers
problems
variety of strategies
2.NBT.7.: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or
the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit
numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens
or hundreds.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to make models of addition and
1. that problems can be solved using models, 1. add and subtract using models, drawings,
subtraction
drawings, and written methods
and a variety of written methods.
2. how to draw addition and subtraction
2. Understand subtraction of 3 digit numbers
3. how to add and subtract using a variety of
written methods
2.NBT.8.: Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. a variety of strategies for mental math in
1. how to apply a variety of strategies in
1. mentally add 10 or 100 to a given number
both addition and subtraction.
mental math to solve addition and
(100-990)
subtraction.
2. mentally subtract 10 or 100 from a given
2. the value of mental math
number (100-990)
2.NBT.9.: Explain why addition and subtraction strategies work, using place value and the properties of operations.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. a variety of addition and subtraction
1. how to communicate the way that
1. explain addition and subtraction strategies
strategies
mathematical strategies work.
2. communicate the strategies through words,
2. there are different methods to
drawing, or pictures.
communicate the mathematical strategies.
Grade 2 – Algebraic Thinking
Essential Questions:
1. How do you use patterns to understand mathematics and model situations?
2. What is algebra?
3. How are the horizontal and vertical axes related?
4. How do algebraic representations relate and compare to one another?
5. How can we communicate and generalize algebraic relationships?
Essential Vocabulary – addition, subtraction, adding to, taking from, putting together, taking apart, comparing, equations, symbol, unknowns, sum,
odd, even, equation, sum, equal addends, doubles, rectangular array, rows, columns, equation, sum, equal addends
We want students to understand how we use patterns and relationships of algebraic representations to generalize, communicate, and
model situations in mathematics.
2.OA.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations within a cultural context,
including those of Montana American Indians, 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.
Students will know…
1. how to add and subtract within 100.
2. how to solve one and two step word
problems.
3. how to solve for unknowns.
4. Montana American Indians are a part of
Montana culture
Grade 2 Enduring Understandings
Students will understand…
3. how to apply addition and subtraction
strategies to solve word problems
4. math applies to the real world, including
cultural components
Students will be able to…
1. add and subtract within 100
2. solve one and two step word problems
3. solve for unknowns
2.OA.2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. basic math facts (within 20)
1. memorization of math facts is a life skill
1. fluently apply their basic math facts
2.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s;
write an equation to express an even number as a sum of two equal addends.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. doubles facts
1. what makes a number odd or even
1. write their doubles facts in equation form
2. odd and even
2. doubles facts always result in an even sum 2. determine whether a number is odd or
3. how to write an equation
even
3. use a variety of strategies
2.OA.4: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation
to express the total as a sum of equal addends.
Grade 2 Enduring Understandings
Students will know…
Students will understand…
Students will be able to…
1. how to make a model of a rectangular
1. that arrays are visual models of equal
1. differentiate between columns and rows
array
addends
2. express the total number of objects within
2. how to add up to 5 equal addends
a given array (up to 5 X 5)
3. how to write an addition equation
3. add and record the equation of up to five
equal addends