# Blog

## Pigs, Chickens, and Algebraic Thinking

Replace the four question marks with the correct numbers in the table below. The proficient third-grader uses arithmetic, and of course, knowledge that pigs have 4 legs and chickens have 2 legs to complete the table with 6 pigs; 9 chickens; 15 animals; and 42 legs.  Another key skill for solving this problem is the… Continue reading Pigs, Chickens, and Algebraic Thinking

## The Area and Perimeter of a Playground

Using this map of a neighborhood playground, find its area in square meters.   Additionally, the neighbors want to build a chain-link fence around the playground.  They can determine the number of meters needed for fencing by finding the perimeter (or distance around) the playground boundaries or the total length of the playground's dimensions. A math… Continue reading The Area and Perimeter of a Playground

## Area of a Playground

A map indicating the shape and dimensions of a small, neighborhood playground is shown below.  Find the area of the playground in square meters. To answer this test question correctly, a student is expected to understand the concept of area (Goal # 9) and compose two shapes mentally into one region.  By adding the area… Continue reading Area of a Playground

## Time Continues On

PROBLEM:  Joshua made a number line to show the times he started and finished his afternoon reading.  The timeline below indicates his starting time and ending time.  He read for an hour.  What was his ending time? A. 3 o'clock B. 3:30 p.m. C. 4:15 p.m. D. 4 o'clock E. 4:15 a.m. Interpreting this timeline… Continue reading Time Continues On

## Reading Tabular Information: Teachers’ Book Shelves

PROBLEM: The table below gives totals for the number of books in 5 third-grade classrooms. One of the teachers is Sarah’s teacher and one is Ben’s teacher. Sarah’s teacher has 20 more books than Ben’s teacher. Who is Sarah’s teacher? Teacher Number of Books Mrs. Alvarez 125 Mr. Benton 132 Ms. Collins 162 Miss Dillard… Continue reading Reading Tabular Information: Teachers’ Book Shelves

## Multiplication Tables and Mathematical Rigor

PROBLEM:  How many vans does it take to transport 63 children on a field trip to a museum if each van carries 9 children? Power-Start Goal #2, knowing the multiplication tables from memory by the end of third grade positions a student well for the upward climb toward math proficiency by 8th grade.  Moreover, the … Continue reading Multiplication Tables and Mathematical Rigor

## Trading Cards and Multiplication Tables

PROBLEM: If you place, on an empty table top, five rows of trading cards with three in each row, then how many cards will be on the table? This problem exemplifies Power-Start Goal #3 of knowing from memory the one-digit multiplication facts and Power-Start Goal #4 use operations (here multiplication) to solve problems.  Knowing the… Continue reading Trading Cards and Multiplication Tables

## Subtraction within 1000: 704 – 356

If a student responds on an end-of-third grade, world-class assessment that 704 -- 356 = 348, then that's an indication of being on track to graduate from high school on par with students from high-achieving nations.  This question involving subtraction within 1000 also indicates that the student meets Power-Start Goal #1 (sense number size &… Continue reading Subtraction within 1000: 704 – 356