# Math - Second Grade

Instructional Tasks

Stand alone tasks are organized to support learning of content standards. These tasks can be used as initial instruction or to support students who are struggling with a particular topic.

Strand: MATHEMATICAL PRACTICES (2.MP)

Strand: OPERATIONS AND ALGEBRAIC THINKING (2.OA)
Represent and solve problems involving addition and subtraction (Standards 2.OA.1)
• A Pencil and a Sticker
This activity poses the question "A pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost together?"
• Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the work advanced second graders might use for adding 2-digit numbers.
Fluently add and subtract within 20 (Standards 2.OA.2).
• Building Toward Fluency
The purpose of this task is to promote certain addition strategies that will help students learn to fluently add and subtract within 20.
Work with equal groups of objects to gain foundations for multiplication (Standards 2.OA.3–4).
• Buttons odd and even
The purpose of this task is for students to determine whether a set of objects (up to 20) has an odd or even number of elements. Students will also write an equation to express an even number as a sum of two equal addends and an odd number as a sum of two equal addends and 1.
• Delayed Gratification
The purpose of this task is for students to compare two options for a prize where the value of one is given \$2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication."
• Partitioning a Rectangle into Unit Squares
The purpose of this task is to show the student that a rectangle can be partitioned into unit squares, and that there are a number of reasonable ways to count the resulting squares.
• Red and Blue Tiles
This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Strand: NUMBER AND OPERATIONS IN BASE TEN (2.NBT)
Understand place value (Standards 2.NBT.1–4).
• Boxes and Cartons of Pencils
In this task students are given information about quantities of pencils packed in boxes and cartons and asked to solve problems such as "Jem has 1 carton and 4 boxes. How many pencils does Jem have all together?"
• Comparisons 1
This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.
• Comparisons 2
The comparisons here involve sums and differences - not primarily to provide an opportunity to calculate, but rather in order to stimulate studentsâ thinking about the magnitudes of the base-ten units of which numbers are composed.
• Counting Stamps
This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps.
• Digits 2-5-7
This task asks students to use all the digits 5, 7, and 2 to create different 3-digit numbers.
• Largest Number Game
In this task students are told "Dona had cards with the numbers 0 to 9 written on them. She flipped over three of them. Her teacher said: 'If those three numbers are the digits in another number, what is the largest three-digit number you can make?'" Students should be asked to think through possibilities and then draw on their ability to compare three digit numbers to complete the task.
• Making 124
Not all students have seen base-ten blocks. This task should only be used with students who know what they are or have some on-hand to use themselves. Students are asked explain how they found all the possible ways to make 124 using base-ten blocks.
• Number Line Comparisons
The purpose of this task is for students to use the number line to make comparisons between 3-digit numbers. The task is designed, in part, to help students understand how the number line works and that numbers on the right of the number line are greater than numbers on the left.
• Ordering 3-digit numbers
In this task each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number. Each group also contains a two-digit number so that students have to do more than just compare the first digit, the second digit, etc.
• Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the work advanced second graders might use for adding 2-digit numbers.
• Using Pictures to Explain Number Comparisons
The purpose of this task is for students to compare three-digit numbers and explain the comparisons based on the meaning of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
They use place value understanding and properties of operations to add and subtract (Standards 2.NBT.5–9).
• Ford and Logan Add 45+36
This task was designed to give students opportunities to solve a problem and analyze other students solutions while working on adding two-digit numbers.
• How Many Days Until Summer Vacation?
The purpose of the task is to allow children an opportunity to subtract a three-digit number including a zero that requires regrouping.
• Jamir's Penny Jar
The purpose of this task is to help students articulate their addition strategies as in and would be most appropriately used once students have a solid understanding of coin values. It also provides a context where it makes sense to "skip count by 5s and 10s" for the combinations that involve more than one nickel or dime.
• Many Ways to do Addition 2
The purpose of this task is not to teach or model the addition strategies. Rather the purpose of this task is make explicit different ways students can solve problems so that they will be able to find the most efficient strategy in any given situation and increase their addition fluency.
• Peyton and Presley Discuss Addition
This purpose of this task is to support students in developing an understanding of a place value strategy for adding numbers.
• Saving Money 1
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money.
• Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the work advanced second graders might use for adding 2-digit numbers.
• Toll Bridge Puzzle
This task is intended to assess adding of four numbers as given in the standard while still being placed in a problem-solving context. As written this task is instructional; due to the random aspect regarding when the correct route is found, it is not appropriate for assessment.

Strand: MEASUREMENT AND DATA (2.MD)
Measure and estimate lengths in standard units (Standards 2.MD.1–4).
• Determining Length
Within the task students have the opportunity to measure and compare lengths of their own foot and that of a partner.
• How Big is a Foot?
The purpose of this task is to understand the idea of a standard unit of measure and why we use them. It also reinforces the idea that we measure lengths by placing units end-to-end.
Relate addition and subtraction to length (Standards 2.MD.5–6).
• Frog and Toad on the number line
The purpose of this task is for students to use a number line to show why two different sums are equal and to represent that equality with an equation. This task could be used to introduce the idea of representing addition on the number line; the teacher could set up a number line on the board or floor so students can act out where the two amphibious friends end up.
• High Jump Competition
This task was designed to offer multiple entry points and solution strategies as students engage in the problem.
They work with time and money (Standards 2.MD.7–8).
• Alexander, Who Used to be Rich Last Sunday
The purpose of this task is for students to find combinations of coins that total the amounts given in a story.
• Choices, Choices, Choices
The purpose of this task is for students to solve problems involving money with prices given in both dollars and cents.
• Delayed Gratification
The purpose of this task is for students to compare two options for a prize where the value of one is given \$2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication."
• Jamir's Penny Jar
The purpose of this task is to help students articulate their addition strategies as in and would be most appropriately used once students have a solid understanding of coin values. It also provides a context where it makes sense to "skip count by 5s and 10s" for the combinations that involve more than one nickel or dime.
• Math Task: Piggy Banks
Students will find the value of money in piggy banks using the coins, cents, and dollars. They will then arrange the value on a number line.
• Ordering Time
The purpose of this task is for students to practice reading time shown on both digital and analog clocks and to order a given set of times.
• Pet Shop
The purpose of the task is to use the given prices of stuffed animals at the "pet shop" to solve problems using money. The students need to use their coins or bills to help them solve each problem.
• Saving Money 1
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money.
• Susan's Choice
The purpose of this task is to address the concept of opportunity cost through a real world context involving money.
• Visiting the Arcade
The purpose of this task is to introduce students to the characteristics of money in a financial literacy sense as well as to solve problems involving money.
They represent and interpret data (Standards 2.MD.9–10).
• Favorite Ice Cream Flavor
The purpose of this task is for students to represent and interpret categorical data. So this task could be used with advanced first graders or second graders just beginning to work with bar graphs.
• Growing Bean Plants
This task adds some rigor to this common activity, by collecting actual growth data, providing practice for students in measuring and recording length measurements.
• Hand Span Measures
This could be used as a class activity, or students could gather and plot data on separate line plots from different age groups.
• Longest Walk
Given a map, students in this task locate two points and draw a line between them and then calculate the length of the line.

Strand: GEOMETRY (2.G)
Reason with shapes and their attributes. (Standards 2.G.1–3).
• Partitioning a Rectangle into Unit Squares
The purpose of this task is to show the student that a rectangle can be partitioned into unit squares, and that there are a number of reasonable ways to count the resulting squares.
• Polygons
The purpose of this task is to give students practice identifying different types of polygons, namely triangles, quadrilaterals, pentagons, and hexagons.
• Representing Half of a Rectangle
This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.
• Which Pictures Represent One Half?
The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

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