Math Tasks
Level of thinking required by a math problem or task.
Cognitive Demand
A collection of attitudes and beliefs students have about their math potential and abilities that they believe define them.
What is Math Identity?
The digits 0-9 are used to create all numbers. Means “a collection”. When there is enough for a new collection, the group goes to the next place value.
Base 10 Number System
Students focus on the whole number and place value ideas to compute. Strengthens number sense. Students make fewer errors & build their confidence.
Flexible Number Strategies / Reasoning Strategies
Fraction model used to visualize parts of a whole. Students can use drawings of shapes, pattern blocks, or even folded paper.
Area Model
Use these with any problem to help students SEE math concepts, relationships, or patterns. Encourages hands-on or spatial learning.
Visuals / Manipulatives
Use these to increase engagement, show math concepts visually, relate to real life contexts, & help students see different representations or perspectives in math.
Math Read Alouds / Picture Books
A groupable place value model that students can easily take apart or put back together.
Any of the following: Straws bundled, beans in a cup, snap cubes, tens frames and counters.
What type of problem is this?
There are 12 bikes outside. 7 are red and the rest are blue. How many bikes are blue?
Part-Part-Whole Story Problem
Fraction model that uses discrete/individual items as the “whole”. Is helpful for exploring equivalent fractions. Ex: 2/3 of 12 books.
Set Model
Tasks that require basic recall of facts, require limited thinking, very straightforward, or clear what procedure needs to be used.
LOW Cognitive Demand Tasks / Memorization or Procedures without Connections
Students look at four numbers or images and share their reasoning.
Which One Doesn't Belong
The ability to identify a quantity without counting each one. Groupings can help students figure out the amount.
Subitizing
You break each number into parts to multiply, then you add the smaller products together to get your answer. Example: 35x6 = 30x6+5x6
Partial Products or Place Value Strategy
These tasks focus on distributing a quantity equally among a specific number of people or groups. They help students understand fractions as division and can be used in a variety of ways.
Sharing Tasks
Tasks that have more than one correct solution. Require students to think creatively and critically. Can be represented & solved in different ways.
Open-Ended / Rich Tasks
These encourage participation and engagement in math conversations. Can also help students reason, explain, listen, & promote deeper understanding.
Talk Moves & Accountable Talk
The act of counting each object in a set only once. Encourage students to line up objects and touch each object once while counting.
One-to-One Correspondence
You change the numbers in the problem making it easier to solve: 42+68 becomes 40+70.
Compensation
Create a story problem to match this equation.
1/2 x 3/4.
Answers will vary. Examples:
Someone ate 1/4 of a loaf of bread, leaving 3/4 left. If you use 1/2 of what's left to make sandwiches, how much of the loaf have you used?
OR
You are walking 3/4 of a mile. You stop 1/2 way to tie your shoe. How far have you gotten when you stop?
A process that feels challenging but leads to understanding. Students grapple but persevere. Learning goals feel attainable & creates a sense of hope.
Productive Struggle
Short daily routine that provides meaningful practice with computation. Develops Number Sense. Students use number relationships and properties to add, subtract, multiply, & divide.
Number Talk
Number representations with fewer than max number of hundreds or tens. Ex: 126 shown as 1 hundred 1 ten and 16 ones.
Equivalent Groupings
You change the numbers in subtraction problem to make it easier to find the answer using mental math. Example: 101-26 = 100 - 25.
Constant Difference / Sliding
Fractional parts must be same size & same shape. Eg. fractions parts must look exactly the same.
The size of the items in a set matters. Eg. to show half of something all the items have to be the same.
Seeing the numerator and denominator to solve problems. Eg. larger denominator means larger fraction.
Fraction Misconceptions