CORE FOUNDATIONS™
It doesn’t reteach.
It unlocks.
Discussion-based intervention that helps students explain ideas, compare strategies and build understanding, one skill at a time. Teachers guide the conversation, with brief, clear explanations from Howie Hua.
The conversation
is the intervention.
Students explain their reasoning, listen to one another and connect ideas. Shared work makes their thinking visible so the group can compare approaches and the teacher can guide the discussion.
Essential skillsAcross four grade-level courses.
Minutes per skillThree connected, 30-minute sessions.
LanguagesTranslated videos, student pages and prompts.
Figure it out. Talk it through.
Show what you know.
Every skill runs three 30-minute sessions. Follow The Traveling Suitcase, a story about 10-to-1 place value relationships. Discussion comes first, so students build the idea before the procedure.
-
Figure it out
Teams watch a visual pattern, discuss what comes next and investigate a story that gives the mathematics a context.
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Talk it through
Students discuss each problem before working it through. Howie Hua adds brief, clear explanations of the mathematics.
-
Show what you know
Teams unpack an image that connects the story to the skill. Each student then checks understanding and reflects in their Student Journal.
Example: The Traveling Suitcase, Course 1, Skill 1, explores 10-to-1 place value relationships.
93 essential skills.
Four courses.
Four grade-level courses, with three 30-minute sessions for every skill. Explore the skills in each course below.
Course 1
Number & Operations
- Place Value Relationships
- Powers of 10
- Read/Write Decimals
- Compare Decimals
- Round Decimals
- Multiply Whole Numbers
- Divide Whole Numbers
- Decimal Operations
Fractions
- Add/Subtract Fractions
- Fractions as Division
- Multiply Fractions
- Fractional Area
- Compare Products
- Multiplication as Scaling
- Unit Fraction ÷ Whole Number
- Whole Number ÷ Unit Fraction
Geometry & Measurement
- Convert Units
- Volume Concepts
- Count Unit Cubes
- Volume by Multiplication
- Volume Formulas
- Coordinate Plane
- Graph Points
- Shape Properties
Algebra & Functions
- Write Expressions
- Number Patterns
Course 2
Ratios & Proportions
- Ratio Language
- Unit Rates
- Ratio Tables
- Percents
Number & Operations
- Divide Fractions
- Negative Numbers
- Opposites
- Four Quadrants
- Order Rationals
- Order in Context
- Absolute Value
Algebra & Functions
- Write Algebraic Expressions
- Equivalent Expressions
- Solution Sets
- One-Step Equations
- Write Inequalities
- Graph Inequalities
- Indep/Dep Variables
- Equations, Tables, Graphs
Geometry & Measurement
- Surface Area
Statistics & Probability
- Statistical Questions
- Distributions
- Summarize Data
Course 3
Number & Operations
- Add Rationals
- Subtract Rationals
- Multiply Rationals
- Divide Rationals
- Fractions to Decimals
Ratios & Proportions
- Proportional Relationships
- Constant of Proportionality
- Proportional Equations
- Percent Applications
Algebra & Functions
- Combine Like Terms
- Factor Expressions
- Two-Step Equations
- Two-Step Inequalities
Geometry & Measurement
- Scale Drawings
- Construct Triangles
- Geometry of Circles
- Angle Relationships
Statistics & Probability
- Sample Inferences
- Compare Populations
- Probability Concept
Course 4
Algebra & Functions
- Exponent Rules
- Square/Cube Roots
- Scientific Notation
- Slope as Rate
- Slope-Intercept Form
- Solution Cases
- Multi-Step Equations
- Systems Concept
- Solve Systems
- Function Concept
- Compare Functions
- Linear vs Nonlinear
- Model with Lines
Number & Operations
- Rationals and Irrationals
- Approximate Irrationals
Geometry & Measurement
- Congruence
- Graph Transformations
- Similarity
- Triangle Angles
- Apply Pythagorean
- Volume of Solids
Statistics & Probability
- Scatter Plots
- Line of Best Fit
- Slope/Intercept
Know where students
start, grow and finish.
The Skills Diagnostic is given at the beginning, middle and end of each course. Results help teachers identify skills that need attention and follow students’ development over time.
Beginning of course
Identify the skills holding students back.
Middle of course
Check growth and choose which skills to work on next.
End of course
Review how far each student has come, using skill-level results for the class and individual students.
A playbook
for every skill.
The Teacher Playbook is low-prep and step by step: what to say, which prompts draw out thinking, and what comes next.
IN EVERY LANGUAGE
Videos, student pages and prompts are fully translated in 25+ languages, with skill-specific language supports.
PROMPTS TO ELICIT THINKING
“What’s happening in this image?” “Where do you see this skill being used?” Open questions and sentence starters give students a way into the discussion.
A shared workspace.
Groups of three at vertical whiteboards are one example. The focus is on comparing ideas, making reasoning visible and giving every student time to reflect.
TWO WAYS
TO USE IT
Pull-out intervention
Use the three-session sequence to focus on the skills students need.
Alongside Core Curriculum™
Teachers can respond on Flex Day with foundational skills students need.
Explore Core CurriculumStart a conversation.
Connect with the MidSchoolMath team to explore the materials and discuss how intervention can fit your teachers’ and students’ needs.
Sources and notes
Source: MidSchoolMath 2027 Program Guide, pp. 38–45 and 54. The four courses total 93 skills: 26 + 23 + 20 + 24. Building Blocks is an additional course.
The 25+ language and full-translation descriptions apply to Core Foundations videos, student pages and prompts. Core Curriculum has a different set of language supports. The research and EdReports findings presented for Core Curriculum should not be read as a review of Core Foundations.
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