Second Grade - MATH
5: Math
Unit 1: Number Sense
Lesson 2
Patterns in Numbers
Students work with multiple 10x10 number grids composed of equal-size square cells. They color cells on the grid to show counting patterns (by 2s, 5s, 10s) and cut out rows from the grid to place end-to-end, explicitly manipulating rows of squares. Students color or mark numbers on the grids to see how colored cells line up in rows and columns and to practice skip-counting by columns (e.g., counting by 10s).
Lesson 3
Missing Numbers
Students are asked to cut out number-grid pieces and assemble them to create a complete number grid, which requires arranging squares into rows and columns. The materials include a 10x10 grid labeled 1–100 and tasks in which students fill in missing numbers on that grid. Students also complete number-grid puzzles (Option 1 and Option 2) that require recognizing the grid layout and sequencing numbers across rows and columns.
Final Project
Project Number Sense!
Students are asked to include photographs of patterns of objects in the real world with examples that explicitly list tiles, quilts, and brick walls, which are typical rectangular arrays of repeated shapes. The project also asks students to include a number grid from Lesson 2 or other number patterns, and to produce captions using correct mathematical language. Planning and photo-topic sheets prompt students to collect images for "patterns of objects" and "number patterns," and checklist pages require 2–3 photographs for each topic.
Unit 2: Addition and Subtraction/Fact Power!
Lesson 1
Using Arrays to Add
Students label and count rows and columns on the muffin tin (identifying a 4 by 3 array) and on other everyday arrays (egg carton, crayon box). Students draw arrays on laminated grid paper by filling in the correct number of spaces to represent rows and columns (Activity 4) and create and name arrays for given totals (8, 12, 16, 20, 24) on the activity pages. Students find arrays in the neighborhood and build Arrayville buildings using sticky notes to form rows and columns, then write repeated-addition number sentences to count the total.
Lesson 2
So Many More Ways to Add
Students are shown and asked to interpret a 3 × 3 array, write the corresponding repeated-addition sentence (3 + 3 + 3 = 9), and identify the addends and sum. Students are later asked to create a number collection for 15 and are prompted that one representation could be a 3 × 5 array. The Skills section explicitly states that students use addition to find totals of objects arranged in rectangular arrays up to 5 rows and 5 columns and to write the total as a sum of equal addends.
Final Project
Mathematical Ocean Adventure
The project checklist and evaluation rubric explicitly require that students include "an array" and "1 array" in their Mathematical Ocean Adventure story. Directions for the story pages (for example, the "Excitement!" sheet) tell students that each page should include either addition, subtraction, or an array and that they should show their math in words and pictures. The rubric also asks for "Correct math" and points for including an array alongside the required addition and subtraction problems.
Unit 3: Geometry
Lesson 4
Quadrilaterals
Students use geoboards and rubber bands to create rectangles made up of 2 squares and 3 squares and to nest or create squares of different sizes, which involves composing rectangles from same-size squares. In Option 2, students are asked to find how many smallest squares they can make on the geoboard (example given: 36) and to find rectangles of varying sizes, and they record counts with tally marks.
Lesson 6
Fun With Tessellations and Tangrams
The Student Activity Page includes a square grid (Top Right Grid) that students use in Activity 2 to create square tessellation quilts and to color squares in repeating patterns. Activity 2 and the Tessellation Creator link ask students to start with a single shape (including squares) and to fill or manipulate square-based grids to make tessellations. Students are instructed to alternate colors across the square grid, which requires interacting with same-size square units in a rectangular workspace.
Lesson 7
Dividing Shapes
Students use a geoboard to create a long, narrow rectangle and are asked to count how many same-size squares are in it (finding six). They are then challenged to make a rectangle made up of 12 same-size squares and later to create a 15-square rectangle described explicitly as a 3x5 grid. Students are asked to divide these rectangles into halves, thirds, and fourths and to state how many unit squares are in each part (e.g., halves = 6, thirds = 4, fourths = 3).
Unit 5: Measurement: Length
Lesson 1
Why Do We Use Standard Measurement Units?
Students are given a blank 10-by-10 number grid (a rectangle with 10 rows and 10 columns of equal squares) and are asked to write the numbers 1–100 into the correct spaces. The lesson asks students to recognize that each number grid shows 100 numbers and to count by 100s to determine they need 10 such grids to reach 1000. Wrapping-up tasks have students use the same grid to count by tens and fives and to find numbers that are 10 more or 10 less, which relies on the row/column structure of the grid.
Lesson 2
Inches
Students are given a blank 10-by-10 number grid (100 uniform squares) and asked to fill it in with numbers 101–200 after having completed a 1–100 grid. Students place the two completed grids (1–100 and 101–200) side by side and are asked to pick a number between 1 and 10 and count up by tens, pointing to numbers as they go. The student activity pages include a 10x10 grid and tasks that require locating and marking numbers within that rectangular array.
Lesson 3
Inches and Feet
Students are given and use a 10x10 blank grid composed of equally sized squares (100 total) as a Student Activity Page. Students fill number grids sequentially (e.g., completing a grid from 201 to 300 and earlier grids from 1 to 100) and lay three completed 100-grids side by side to represent and count to 300. The grid structure and counting tasks require students to work with rows and columns of same-size squares while numbering and counting them.
Lesson 4
The Metric System, Too
Students are asked to complete a number grid starting at 301 and ending at 400, and the wrapping up directions ask them to lay out four finished number grids showing numbers 1 through 400. The Student Activity Page description explicitly shows a blank 10x10 grid of uniform squares (totaling 100 squares). The grid is used for numbering and organizing numbers, which requires students to work within rows and columns of same-size squares.
Lesson 5
More Work With Measurement Units
Students use and complete a 10 by 10 number grid (the Student Activity Page) that is described as a layout of 100 equally sized squares. The introduction and activities ask students to fill in number grids (e.g., 401–500) and later lay out five finished number grids to count by hundreds. The Student Activity Page description explicitly notes the grid consists of rows and columns forming a total of 100 squares.
Lesson 7
The Right Tools for the Job
Students complete a 10-by-10 blank number grid made of 100 equal-size squares by filling in numbers (e.g., continuing from 601 to 700). Students lay out all completed number grids (seven grids totaling 700) and count aloud while pointing to individual squares, including counting a sequence from 585 to 615. The activity uses rows and columns implicitly by having students work within a row/column numbered grid.
Lesson 8
Comparing Lengths
Students use a 10-by-10 blank grid (10 columns and 10 rows) that is described as forming a total of 100 squares, and they are instructed to complete number grids (e.g., filling one from 701 to 800). The lesson asks students to lay out all eight completed number grids and notes that together they begin at 1 and end at 800, implying counting across multiple 10x10 grids. The activities require students to fill and count numbers in the grid and to skip-count by 2s and 5s within the grid.
Lesson 9
Gummy Worms and Measurement Data
Students are given a large 10-by-10 number grid (100 uniform small squares) as a Student Activity Page and are asked to complete number grids beginning at 801 and to lay out all completed number grids totaling 9 grids (ending at 900). Students are asked to count by hundreds from 100 to 900 while pointing to the numbers on the completed grids. The grid description explicitly notes 10 rows and 10 columns creating 100 small squares.
Lesson 10
Measurement Practice and Problem Solving
The Student Activity Page includes a blank 10-by-10 grid of equal-sized squares that students are instructed to complete with consecutive numbers. Students are asked to count by 1s from 980 to 1000 within the grid and later to lay out all ten completed number grids (ten 10x10 grids) and note that they have written 1000 numbers. The Wrapping Up tasks ask students to count by 10s and 100s using the arranged grids and to point to numbers that are 10 more/less, which has them interact with rows/columns of the grids.
Unit 9: Data and Graphing
Lesson 5
More Graphing Practice
Students use a blank bar graph that is a grid with horizontal and vertical lines (squares) and are instructed to write numbers 1–10 on the left and numbers of letters across the bottom, then color bars that reach a given number (e.g., color a bar that reaches "3" above the number 4). Activity 4 asks students to use laminated grid paper and a dry-erase marker to create bars on the grid or mark spaces for a line plot and suggests turning the grid horizontal for a longer range. The instructions for making bar graphs require students to color or fill in the grid squares to represent counts.
Unit 10: Skills Review
Lesson 4
Reviewing Geometry
Activity 2 asks students to make a rectangle made up of 2 squares and a rectangle made up of 3 squares, and the student sheet asks students to draw lines to partition rectangles and other shapes into halves, thirds, and fourths. The lesson gives students geoboards and rubber bands to create plane shapes and to practice partitioning a square and rectangles into equal parts. The partitioning activity explicitly has students produce shapes composed of multiple equal pieces (including multiple squares).
6: Reading
Unit 2: Semester 2
Lesson 14
Words Starting with q or a
Students are introduced to a calendar as "a chart or grid that shows the days in each month" (Activity 2.1). In Day 5 Activity 5.1 students cut, tape, and write the days of the week into a pre-made calendar grid, and Student Activity Page descriptions include explicit grids (a 5x4 grid and a 4x4 grid) for student use. Several activities direct students to place or write items into the boxes of those grids (e.g., adding days of the week to calendar squares).